diff --git a/apps/yaak-client/components/ContextMenus.tsx b/apps/yaak-client/components/ContextMenus.tsx
index b9e15773..dd8bad8f 100644
--- a/apps/yaak-client/components/ContextMenus.tsx
+++ b/apps/yaak-client/components/ContextMenus.tsx
@@ -8,12 +8,15 @@ export function ContextMenus() {
   const menus = useAtomValue(contextMenusAtom);
   return (
     <>
-      {menus.map(({ id, items, triggerPosition, triggerRect }) => (
+      {menus.map(({ id, items, triggerPosition, triggerRect, triggerEl }) => (
         <ErrorBoundary key={id} name={`ContextMenu ${id}`}>
           <ContextMenu
             items={items}
             triggerPosition={triggerPosition}
             triggerRect={triggerRect}
+            // The trigger isn't a React component here, so it arrives as an element and gets
+            // wrapped to look like the ref the menu expects
+            triggerRef={{ current: triggerEl ?? null }}
             onClose={() => hideContextMenu(id)}
           />
         </ErrorBoundary>
diff --git a/apps/yaak-client/components/core/Dropdown.tsx b/apps/yaak-client/components/core/Dropdown.tsx
index e6de0c6c..a1836206 100644
--- a/apps/yaak-client/components/core/Dropdown.tsx
+++ b/apps/yaak-client/components/core/Dropdown.tsx
@@ -242,13 +242,20 @@ export interface ContextMenuProps {
    * from a button.
    */
   triggerRect?: Pick<DOMRect, "top" | "bottom" | "left" | "right">;
+  /**
+   * The element the menu belongs to, so a click on it doesn't count as a click outside.
+   *
+   * Without this the trigger gets both: the outside-click handler closes the menu on mousedown,
+   * then the trigger's own click opens it again, and pressing it looks like it does nothing.
+   */
+  triggerRef?: RefObject<HTMLElement | null>;
   className?: string;
   items: DropdownProps["items"];
   onClose: () => void;
 }
 
 export const ContextMenu = forwardRef<DropdownRef, ContextMenuProps>(function ContextMenu(
-  { triggerPosition, triggerRect, className, items, onClose },
+  { triggerPosition, triggerRect, triggerRef, className, items, onClose },
   ref,
 ) {
   const triggerShape = useMemo(
@@ -275,6 +282,7 @@ export const ContextMenu = forwardRef<DropdownRef, ContextMenuProps>(function Co
       ref={ref}
       items={items}
       onClose={onClose}
+      triggerRef={triggerRef}
       triggerShape={triggerShape}
     />
   );
@@ -290,7 +298,9 @@ interface MenuProps {
   fullWidth?: boolean;
   isOpen: boolean;
   items: DropdownItem[];
-  triggerRef?: RefObject<HTMLButtonElement | null>;
+  // Any element, not just a button: a menu can be opened from anything, and this is only ever
+  // used to ask whether a click landed on the trigger
+  triggerRef?: RefObject<HTMLElement | null>;
   isSubmenu?: boolean;
 }
 
diff --git a/apps/yaak-client/components/core/Editor/Editor.tsx b/apps/yaak-client/components/core/Editor/Editor.tsx
index 606136af..a472f938 100644
--- a/apps/yaak-client/components/core/Editor/Editor.tsx
+++ b/apps/yaak-client/components/core/Editor/Editor.tsx
@@ -43,6 +43,7 @@ import { IconButton } from "../IconButton";
 import "./Editor.css";
 import {
   baseExtensions,
+  editableExtensions,
   getLanguageExtension,
   multiLineExtensions,
   readonlyExtensions,
@@ -289,7 +290,7 @@ function EditorInner({
     function configureReadOnly() {
       if (cm.current === null) return;
       const current = readOnlyCompartment.current.get(cm.current.view.state) ?? emptyExtension;
-      const next = readOnly ? readonlyExtensions : emptyExtension;
+      const next = readOnly ? readonlyExtensions : editableExtensions;
       // PERF: This is expensive with hundreds of editors on screen, so only do it when necessary
       if (current === next) return;
 
@@ -412,7 +413,7 @@ function EditorInner({
           keymapCompartment.current.of(
             keymapExtensions[settings.editorKeymap] ?? keymapExtensions.default,
           ),
-          readOnlyCompartment.current.of(readOnly ? readonlyExtensions : emptyExtension),
+          readOnlyCompartment.current.of(readOnly ? readonlyExtensions : editableExtensions),
           ...getExtensions({
             container,
             singleLine,
diff --git a/apps/yaak-client/components/core/Editor/extensions.ts b/apps/yaak-client/components/core/Editor/extensions.ts
index 95904089..29be56cb 100644
--- a/apps/yaak-client/components/core/Editor/extensions.ts
+++ b/apps/yaak-client/components/core/Editor/extensions.ts
@@ -59,7 +59,7 @@ import { pluralizeCount } from "../../../lib/pluralize";
 import { showGraphQLDocExplorerAtom } from "../../graphql/graphqlAtoms";
 import type { EditorProps } from "./Editor";
 import { jsonParseLinter } from "./json-lint";
-import { largeValues } from "./largeValues";
+import { largeValues, mediaValues } from "./largeValues";
 import { pairs } from "./pairs/extension";
 import { searchMatchCount } from "./searchMatchCount";
 import { text } from "./text/extension";
@@ -259,10 +259,19 @@ export const baseExtensions = [
 export const readonlyExtensions = [
   EditorState.readOnly.of(true),
   EditorView.contentAttributes.of({ tabindex: "-1" }),
-  // Read-only only, so we never hide part of a document someone is editing
+  // Nobody is editing this, so every rule applies
   largeValues,
 ];
 
+/**
+ * The counterpart for a document being edited.
+ *
+ * Only encoded media collapses here: it is pasted rather than typed, and replaced rather than
+ * edited, so a tag stands in for it without hiding anything anyone meant to read. The rules that
+ * hide text by length alone stay out. See {@link mediaValues}.
+ */
+export const editableExtensions = [mediaValues];
+
 export const multiLineExtensions = ({ hideGutter }: { hideGutter?: boolean }) => [
   search({ top: true }),
   searchMatchCount(),
diff --git a/apps/yaak-client/components/core/Editor/largeValues.test.ts b/apps/yaak-client/components/core/Editor/largeValues.test.ts
index 59a6bd81..6df9f0aa 100644
--- a/apps/yaak-client/components/core/Editor/largeValues.test.ts
+++ b/apps/yaak-client/components/core/Editor/largeValues.test.ts
@@ -1,6 +1,7 @@
 import { EditorState } from "@codemirror/state";
 import { jsonc } from "@shopify/lang-jsonc";
 import { text } from "./text/extension";
+import { twig } from "./twig/extension";
 import { describe, expect, test } from "vite-plus/test";
 import {
   COLLAPSE_MEDIA_CHARS,
@@ -256,9 +257,15 @@ describe("sniffing the collapsed value", () => {
     expect(widget?.sniffed).toMatchObject({ label: "PNG" });
   });
 
-  test("names nothing when a column cut lands mid-line after other text", () => {
-    const state = plainState(`some prefix text ${pngBase64()}`);
-    expect(widgets(state)[0]?.sniffed).toBeNull();
+  test("finds a run that starts partway through a line, and names it", () => {
+    // No grammar here, and the value is not the whole line. The run is found by its alphabet,
+    // so the prefix stays on screen and the blob is still named.
+    const prefix = "some prefix text ";
+    const state = plainState(`${prefix}${pngBase64()}`);
+    const [widget] = widgets(state);
+
+    expect(widget?.valueFrom).toBe(prefix.length);
+    expect(widget?.sniffed).toMatchObject({ label: "PNG" });
   });
 });
 
@@ -343,6 +350,126 @@ describe("media collapsing, below the length rules", () => {
   });
 });
 
+describe("media rule only, for a document being edited", () => {
+  /** What an editable editor gets: rule 2 alone */
+  function editableRanges(state: EditorState) {
+    const ranges: { from: number; to: number }[] = [];
+    const iter = collapseDecorations(state, [{ from: 0, to: state.doc.length }], "media").iter();
+    while (iter.value != null) {
+      ranges.push({ from: iter.from, to: iter.to });
+      iter.next();
+    }
+    return ranges;
+  }
+
+  function png(bytes: number) {
+    const b = new Uint8Array(bytes);
+    b.set([0x89, 0x50, 0x4e, 0x47, 0x0d, 0x0a, 0x1a, 0x0a]);
+    let binary = "";
+    for (const byte of b) binary += String.fromCharCode(byte);
+    return btoa(binary);
+  }
+
+  test("collapses a pasted image, the one thing it is for", () => {
+    const value = png(3_000);
+    const state = jsonState(`{\n  "avatar": "${value}"\n}`);
+
+    expect(editableRanges(state)).toHaveLength(1);
+    expect(state.sliceDoc(editableRanges(state)[0]!.from, editableRanges(state)[0]!.to)).toBe(
+      value,
+    );
+  });
+
+  test("leaves a long value alone when nothing can name it", () => {
+    // Rule 1 would take this on a stalling line. Editing it is plausible, so it stays.
+    const doc = `{"blob":"${"Z".repeat(COLLAPSE_TOKEN_CHARS * 3)}"}`;
+    expect(doc.length).toBeGreaterThan(MAX_VISIBLE_LINE_CHARS);
+    expect(editableRanges(jsonState(doc))).toEqual([]);
+  });
+
+  test("never cuts at the column limit, which would strand text out of reach", () => {
+    // Rule 3 territory: a minified body with no value big enough to collapse on its own
+    const doc = `[${Array.from({ length: 4_000 }, (_, i) => `"word-${i}"`).join(",")}]`;
+    expect(doc.length).toBeGreaterThan(MAX_VISIBLE_LINE_CHARS);
+    expect(editableRanges(jsonState(doc))).toEqual([]);
+    // The read-only rules still cut it
+    expect(collapsedRanges(jsonState(doc))).toHaveLength(1);
+  });
+
+  test("never swallows a template tag, collapsing only the run beside it", () => {
+    // A brace is not in the base64 alphabet, so the run starts after the tag and the tag stays
+    // on screen where it can still be read and edited
+    const tag = "{{ image }}";
+    const doc = `{"avatar":"${tag}${png(3_000)}"}`;
+    const ranges = editableRanges(jsonState(doc));
+
+    expect(ranges).toHaveLength(1);
+    expect(ranges[0]!.from).toBe(doc.indexOf(tag) + tag.length);
+    expect(doc.slice(ranges[0]!.from, ranges[0]!.to)).not.toContain("{");
+  });
+
+  test("finds a data URI whole, header and all", () => {
+    const value = `data:image/jpeg;base64,${png(3_000)}`;
+    const doc = `{"avatar":"${value}"}`;
+    const ranges = editableRanges(jsonState(doc));
+
+    expect(ranges).toHaveLength(1);
+    expect(doc.slice(ranges[0]!.from, ranges[0]!.to)).toBe(value);
+  });
+
+  test("hides no line break, so the plugin may provide it from the viewport", () => {
+    const state = jsonState(`{\n  "a": "${png(3_000)}",\n  "b": 1\n}`);
+    for (const { from, to } of editableRanges(state)) {
+      expect(state.sliceDoc(from, to)).not.toContain("\n");
+    }
+  });
+});
+
+describe("templated fields, where the grammar is an overlay", () => {
+  // Every editable field mixes its language with twig, which mounts the base language as an
+  // overlay. Overlays are not traversed by `Tree.iterate`, so a rule that walks the tree sees
+  // one enormous Text node and finds nothing. Rule 2 reads the text instead, and this is the
+  // case that has to keep working: an image pasted into a JSON request body.
+  const twigState = (doc: string) =>
+    EditorState.create({
+      doc,
+      extensions: [
+        twig({
+          base: jsonc(),
+          environmentVariables: [],
+          completionOptions: [],
+          onClickVariable: () => {},
+          onClickMissingVariable: () => {},
+          onClickPathParameter: () => {},
+          extraExtensions: [],
+        }),
+        largeValues,
+      ],
+    });
+
+  function png(bytes: number) {
+    const b = new Uint8Array(bytes);
+    b.set([0x89, 0x50, 0x4e, 0x47, 0x0d, 0x0a, 0x1a, 0x0a]);
+    let binary = "";
+    for (const byte of b) binary += String.fromCharCode(byte);
+    return btoa(binary);
+  }
+
+  test("collapses a pasted image in a templated body", () => {
+    const value = png(3_000);
+    const state = twigState(`{\n  "avatar": "${value}"\n}`);
+    const ranges: { from: number; to: number }[] = [];
+    const iter = collapseDecorations(state, [{ from: 0, to: state.doc.length }], "media").iter();
+    while (iter.value != null) {
+      ranges.push({ from: iter.from, to: iter.to });
+      iter.next();
+    }
+
+    expect(ranges).toHaveLength(1);
+    expect(state.sliceDoc(ranges[0]!.from, ranges[0]!.to)).toBe(value);
+  });
+});
+
 describe("viewport scoping", () => {
   const doc = () => {
     const value = "A".repeat(COLLAPSE_TOKEN_CHARS * 2);
diff --git a/apps/yaak-client/components/core/Editor/largeValues.ts b/apps/yaak-client/components/core/Editor/largeValues.ts
index d9635acc..49185997 100644
--- a/apps/yaak-client/components/core/Editor/largeValues.ts
+++ b/apps/yaak-client/components/core/Editor/largeValues.ts
@@ -64,10 +64,22 @@ export const COLLAPSE_MEDIA_CHARS = 1_000;
  * gives its format up in the first dozen bytes — so the tag can name the format and open the
  * value in the matching viewer without any of it being read. See {@link sniffValue}.
  *
- * Read-only editors only. Hiding part of a document someone is editing would mean editing
- * text they can't see.
+ * An editable document gets rule 2 alone, as {@link mediaValues}. Encoded media is never typed
+ * by hand: it arrives pasted, and the only edit anyone makes to it is replacing it wholesale,
+ * which the tag already supports — {@link EditorView.atomicRanges} makes it delete as one unit.
+ * So collapsing it hides nothing anyone was going to read. The other two rules stay out, since
+ * they hide text by length alone, without being able to say what it is: under rule 3 a minified
+ * body would become uneditable past the column limit, which really would be editing text you
+ * can't see.
  */
 
+/**
+ * Which of the three rules to apply.
+ *
+ * `media` is the subset safe for a document being edited: collapse only what we can name.
+ */
+export type CollapseRules = "all" | "media";
+
 /**
  * A hidden range, the value it belongs to, and what that value turned out to be.
  *
@@ -101,7 +113,7 @@ const CHEVRON_DOWN =
  * A span with a role rather than a real button, because a button's box model makes the line
  * taller — the one thing this extension exists to keep from happening.
  */
-function makeTagButton(el: HTMLElement, title: string, onOpen: (at: DOMRect) => void) {
+function makeTagButton(el: HTMLElement, title: string, onOpen: () => void) {
   el.role = "button";
   el.ariaHasPopup = "menu";
   el.tabIndex = 0;
@@ -116,13 +128,13 @@ function makeTagButton(el: HTMLElement, title: string, onOpen: (at: DOMRect) =>
   el.addEventListener("click", (e) => {
     e.preventDefault();
     e.stopPropagation();
-    onOpen(el.getBoundingClientRect());
+    onOpen();
   });
   el.addEventListener("keydown", (e) => {
     if (e.key !== "Enter" && e.key !== " ") return;
     e.preventDefault();
     e.stopPropagation();
-    onOpen(el.getBoundingClientRect());
+    onOpen();
   });
 }
 
@@ -177,7 +189,7 @@ class LargeValueWidget extends WidgetType {
     makeTagButton(
       el,
       this.sniffed == null ? "Value actions" : `${this.sniffed.label} actions`,
-      (rect) => fireAndForget(this.openMenu(view, rect)),
+      () => fireAndForget(this.openMenu(view, el)),
     );
 
     return el;
@@ -190,11 +202,8 @@ class LargeValueWidget extends WidgetType {
    * neither the React menu nor the viewers behind the dialog are worth carrying until someone
    * asks for them.
    */
-  private async openMenu(
-    view: EditorView,
-    rect: Pick<DOMRect, "top" | "bottom" | "left" | "right">,
-  ) {
-    const [{ showContextMenu }, { showLargeValueDialog }, { encodingLabel, largeValueActions }] =
+  private async openMenu(view: EditorView, tag: HTMLElement) {
+    const [{ toggleContextMenu }, { showLargeValueDialog }, { encodingLabel, largeValueActions }] =
       await Promise.all([
         import("../../../lib/contextMenu"),
         import("../../LargeValueDialog"),
@@ -209,11 +218,13 @@ class LargeValueWidget extends WidgetType {
       Math.min(this.valueFrom + SNIFF_HEAD_CHARS, this.to),
     );
 
-    showContextMenu({
+    // The whole tag, so the menu can align to whichever edge has room beside it
+    const rect = tag.getBoundingClientRect();
+    toggleContextMenu({
       id: "large-value",
-      // The whole tag, so the menu can align to whichever edge has room beside it
       triggerPosition: { x: rect.left, y: rect.bottom },
       triggerRect: rect,
+      triggerEl: tag,
       items: [
         { type: "separator", label: encodingLabel(head, sniffed, this.to - this.from) },
         ...largeValueActions({
@@ -344,25 +355,68 @@ function treeForLines(state: EditorState, lines: Line[]): SyntaxTree {
 
 const QUOTES = ['"', "'", "`"];
 
+/** A run of base64, long enough to be worth looking at. Nothing else can be encoded media. */
+const ENCODED_RUN = new RegExp(`[A-Za-z0-9+/=_-]{${COLLAPSE_MEDIA_CHARS},}`, "g");
+
+/** The header that turns a bare run into a data URI, when one sits right before it. */
+const DATA_URI_HEAD = /data:[^,;\s"']*(?:;[^,;\s"']*)*;base64,$/;
+
 /**
- * Quoted values on this line worth collapsing, in document order.
+ * Encoded media on this line, found by reading the text rather than the grammar.
  *
- * Everything between the quotes goes, so a long string reads as `"image": "<tag>"` and the key
- * still tells you what it is. Undelimited tokens are left to the column cut instead: replacing
- * one whole would leave the line with nothing on it but a tag.
+ * Deliberately grammar-free. Every editable field in the app mixes its language with the twig
+ * parser, which mounts the base language as an *overlay*, and overlays are not traversed by
+ * `Tree.iterate` — so a rule that walks the tree finds one enormous `Text` node and nothing
+ * inside it. Rule 2 has to work in those fields above all, since that is where images get
+ * pasted, and a run of base64 is a text pattern anyway: no grammar can describe it better than
+ * the alphabet does.
+ *
+ * A `data:` header is picked up by looking backwards from the run, so the whole URI collapses
+ * as one thing and its declared type is what names it.
  */
-function findCollapsibleTokens(state: EditorState, tree: SyntaxTree, line: Line): Collapse[] {
+function findMediaRuns(state: EditorState, line: Line): Collapse[] {
+  const text = state.sliceDoc(line.from, line.to);
+  const collapses: Collapse[] = [];
+
+  ENCODED_RUN.lastIndex = 0;
+  for (let m = ENCODED_RUN.exec(text); m != null; m = ENCODED_RUN.exec(text)) {
+    let start = m.index;
+    // A data URI's own header breaks the alphabet, so the run starts after it
+    const header = DATA_URI_HEAD.exec(text.slice(0, start));
+    if (header != null) {
+      start = header.index;
+    }
+
+    const valueFrom = line.from + start;
+    const valueTo = line.from + m.index + m[0].length;
+    const head = state.sliceDoc(valueFrom, Math.min(valueFrom + SNIFF_HEAD_CHARS, valueTo));
+    const sniffed = sniffValue(head);
+
+    // Only hide what we can name. A short magic number matches by chance now and then, so the
+    // run itself has to look encoded too.
+    if (sniffed != null && sniffed.encoding === "base64" && isEncodedRun(head, sniffed.offset)) {
+      collapses.push({ from: valueFrom, to: valueTo, valueFrom, sniffed });
+    }
+  }
+
+  return collapses;
+}
+
+/**
+ * Quoted values big enough to be a rendering problem on their own, whatever they hold.
+ *
+ * Needs the grammar, to find where the value starts and ends, and so only runs for a document
+ * nobody is editing — which is also the only place this rule applies.
+ */
+function findLargeTokens(state: EditorState, tree: SyntaxTree, line: Line): Collapse[] {
   const collapses: Collapse[] = [];
-  // Length alone only hides things on a line that would stall without it. On a line that renders
-  // fine, being long is not a reason to hide something we can't even name.
-  const stalls = line.to - line.from > MAX_VISIBLE_LINE_CHARS;
 
   tree.iterate({
     from: line.from,
     to: line.to,
     enter: (node) => {
       // A node this small can't contain anything worth collapsing, and neither can its children
-      if (node.to - node.from < COLLAPSE_MEDIA_CHARS) return false;
+      if (node.to - node.from < COLLAPSE_TOKEN_CHARS) return false;
       // Only leaves, so we collapse the string itself rather than the object holding it
       if (node.node.firstChild != null) return true;
 
@@ -375,21 +429,10 @@ function findCollapsibleTokens(state: EditorState, tree: SyntaxTree, line: Line)
       // Everything inside the quotes. The whole value is hidden, so it is its own value range
       const valueFrom = from + 1;
       const valueTo = to - 1;
-      if (valueTo <= valueFrom) return false;
+      if (valueTo - valueFrom < COLLAPSE_TOKEN_CHARS) return false;
 
-      // The head is all it takes, so this never reads the value it describes
       const head = state.sliceDoc(valueFrom, Math.min(valueFrom + SNIFF_HEAD_CHARS, valueTo));
-      const sniffed = sniffValue(head);
-
-      // Big enough to be a rendering problem on its own, or something we can both name and be
-      // sure is encoded — a short magic number matches by chance, and hiding text would be worse
-      // than showing base64
-      const oversized = stalls && valueTo - valueFrom >= COLLAPSE_TOKEN_CHARS;
-      const media =
-        sniffed != null && sniffed.encoding === "base64" && isEncodedRun(head, sniffed.offset);
-      if (oversized || media) {
-        collapses.push({ from: valueFrom, to: valueTo, valueFrom, sniffed });
-      }
+      collapses.push({ from: valueFrom, to: valueTo, valueFrom, sniffed: sniffValue(head) });
       return false;
     },
   });
@@ -397,6 +440,23 @@ function findCollapsibleTokens(state: EditorState, tree: SyntaxTree, line: Line)
   return collapses;
 }
 
+/**
+ * Both rules' findings as one list, in document order, with nothing overlapping.
+ *
+ * A big quoted base64 value satisfies both rules, and two decorations over the same text is an
+ * error. The token wins where they collide, because its range stops at the quotes and so leaves
+ * the structure around it readable.
+ */
+function mergeCollapses(tokens: Collapse[], runs: Collapse[]): Collapse[] {
+  const merged = [...tokens];
+  for (const run of runs) {
+    if (!tokens.some((t) => run.from < t.to && t.from < run.to)) {
+      merged.push(run);
+    }
+  }
+  return merged.sort((a, b) => a.from - b.from);
+}
+
 /**
  * Where the line runs past the column limit, counting only what is still visible after the
  * token collapses, or -1 if it fits.
@@ -421,10 +481,21 @@ function findColumnCut(line: Line, tokens: Collapse[]): number {
   return -1;
 }
 
-function collapsesForLine(state: EditorState, tree: SyntaxTree, line: Line): Collapse[] {
-  const tokens = findCollapsibleTokens(state, tree, line);
-  if (line.to - line.from <= MAX_VISIBLE_LINE_CHARS) {
-    return tokens; // Short enough to render, so there is nothing left to cut
+function collapsesForLine(
+  state: EditorState,
+  tree: SyntaxTree,
+  line: Line,
+  rules: CollapseRules,
+): Collapse[] {
+  const runs = findMediaRuns(state, line);
+  // Length alone only hides things on a line that would stall without it, and never in a
+  // document being edited, where hiding text by size would put it out of reach
+  const stalls = rules === "all" && line.to - line.from > MAX_VISIBLE_LINE_CHARS;
+  const tokens = mergeCollapses(stalls ? findLargeTokens(state, tree, line) : [], runs);
+
+  // Short enough to render, so there is nothing left to cut
+  if (!stalls) {
+    return tokens;
   }
 
   const cut = findColumnCut(line, tokens);
@@ -450,6 +521,7 @@ function collapsesForLine(state: EditorState, tree: SyntaxTree, line: Line): Col
 export function collapseDecorations(
   state: EditorState,
   ranges: readonly { from: number; to: number }[],
+  rules: CollapseRules = "all",
 ): DecorationSet {
   const lines = collapsibleLines(state, ranges);
   if (lines.length === 0) {
@@ -459,7 +531,7 @@ export function collapseDecorations(
   const tree = treeForLines(state, lines);
   const decorations: Range<Decoration>[] = [];
   for (const line of lines) {
-    for (const { from, to, valueFrom, sniffed } of collapsesForLine(state, tree, line)) {
+    for (const { from, to, valueFrom, sniffed } of collapsesForLine(state, tree, line, rules)) {
       const widget = new LargeValueWidget(from, to, valueFrom, sniffed);
       decorations.push(Decoration.replace({ widget }).range(from, to));
     }
@@ -473,30 +545,40 @@ export function collapseDecorations(
  * Recomputed when the document changes, when the viewport moves, and when background parsing
  * advances — a value can only be found once the grammar has reached it.
  */
-const largeValuePlugin = ViewPlugin.fromClass(
-  class {
-    decorations: DecorationSet;
+function collapsePlugin(rules: CollapseRules) {
+  return ViewPlugin.fromClass(
+    class {
+      decorations: DecorationSet;
 
-    constructor(view: EditorView) {
-      this.decorations = collapseDecorations(view.state, view.visibleRanges);
-    }
-
-    update(update: ViewUpdate) {
-      if (
-        update.docChanged ||
-        update.viewportChanged ||
-        syntaxTree(update.startState) !== syntaxTree(update.state)
-      ) {
-        this.decorations = collapseDecorations(update.view.state, update.view.visibleRanges);
+      constructor(view: EditorView) {
+        this.decorations = collapseDecorations(view.state, view.visibleRanges, rules);
       }
-    }
-  },
-  {
-    decorations: (v) => v.decorations,
-    // Step the cursor over a placeholder instead of stranding it inside
-    provide: (plugin) =>
-      EditorView.atomicRanges.of((view) => view.plugin(plugin)?.decorations ?? Decoration.none),
-  },
-);
 
-export const largeValues: Extension = [largeValuePlugin];
+      update(update: ViewUpdate) {
+        if (
+          update.docChanged ||
+          update.viewportChanged ||
+          syntaxTree(update.startState) !== syntaxTree(update.state)
+        ) {
+          this.decorations = collapseDecorations(
+            update.view.state,
+            update.view.visibleRanges,
+            rules,
+          );
+        }
+      }
+    },
+    {
+      decorations: (v) => v.decorations,
+      // Step the cursor over a placeholder instead of stranding it inside, and delete it whole
+      provide: (plugin) =>
+        EditorView.atomicRanges.of((view) => view.plugin(plugin)?.decorations ?? Decoration.none),
+    },
+  );
+}
+
+/** All three rules. For a document nobody is editing. */
+export const largeValues: Extension = [collapsePlugin("all")];
+
+/** Only what we can name, which is the part that is safe to hide while someone is editing. */
+export const mediaValues: Extension = [collapsePlugin("media")];
diff --git a/apps/yaak-client/lib/contextMenu.ts b/apps/yaak-client/lib/contextMenu.ts
index c465fa3d..cfff79f4 100644
--- a/apps/yaak-client/lib/contextMenu.ts
+++ b/apps/yaak-client/lib/contextMenu.ts
@@ -16,6 +16,8 @@ export interface ContextMenuInstance {
   triggerPosition: { x: number; y: number };
   /** The trigger's box, when it has one, so placement can align to its edges */
   triggerRect?: Pick<DOMRect, "top" | "bottom" | "left" | "right">;
+  /** The element it belongs to, so clicking that doesn't read as a click outside */
+  triggerEl?: HTMLElement | null;
   items: DropdownItem[];
 }
 
@@ -25,6 +27,20 @@ export function showContextMenu({ id, ...props }: ContextMenuInstance) {
   jotaiStore.set(contextMenusAtom, (m) => [...m.filter((c) => c.id !== id), { id, ...props }]);
 }
 
+/**
+ * Opens the menu, or closes it if this one is already open.
+ *
+ * What a trigger wants: pressing it a second time should put the menu away. Same shape as
+ * {@link toggleDialog}.
+ */
+export function toggleContextMenu({ id, ...props }: ContextMenuInstance) {
+  if (jotaiStore.get(contextMenusAtom).some((c) => c.id === id)) {
+    hideContextMenu(id);
+  } else {
+    showContextMenu({ id, ...props });
+  }
+}
+
 export function hideContextMenu(id: string) {
   jotaiStore.set(contextMenusAtom, (m) => m.filter((c) => c.id !== id));
 }
diff --git a/apps/yaak-client/lib/largeValue.ts b/apps/yaak-client/lib/largeValue.ts
index 1bd663fe..3e4a0cf4 100644
--- a/apps/yaak-client/lib/largeValue.ts
+++ b/apps/yaak-client/lib/largeValue.ts
@@ -60,10 +60,23 @@ export function largeValueActions({
     });
   }
 
+  // Two ways to copy a picture, because either can be the one you wanted: the image to paste
+  // somewhere that takes one, or the text to paste back into a request
+  const image = isCopyableImage(sniffed);
+  if (image) {
+    items.push({
+      label: "Copy Image",
+      leftSlot: createElement(Icon, { icon: "copy" }),
+      onSelect: () => copyImage(value(), sniffed, copyText()),
+    });
+  }
+
   items.push({
-    label: sniffed?.mime.startsWith("image/") ? "Copy Image" : "Copy",
-    leftSlot: createElement(Icon, { icon: "copy" }),
-    onSelect: () => copyValue(value(), sniffed, copyText()),
+    label: sniffed?.encoding === "base64" ? "Copy Base64" : "Copy",
+    // Second of a pair reads as one thing with two options, so it keeps the indent without
+    // repeating the icon above it
+    leftSlot: createElement(Icon, { icon: image ? "empty" : "copy" }),
+    onSelect: () => copyToClipboard(copyText()),
   });
 
   items.push({
@@ -167,15 +180,15 @@ async function toPngBlob(text: string, sniffed: SniffedValue): Promise<Blob> {
 }
 
 /**
- * Copies the value: the picture itself when it is one, and the text it stands for otherwise.
+ * Puts the picture on the clipboard, so it can be pasted anywhere that takes an image.
  *
  * Not awaited, and deliberately so. The webview only allows a clipboard write that starts inside
  * the click that asked for it, and decoding a few megabytes takes longer than that lasts — so
  * the item is handed the still-pending promise rather than a finished blob.
  */
-export function copyValue(text: string, sniffed: SniffedValue | null, hidden: string) {
-  if (!isCopyableImage(sniffed) || typeof ClipboardItem === "undefined") {
-    copyToClipboard(hidden);
+export function copyImage(text: string, sniffed: SniffedValue, fallback: string) {
+  if (typeof ClipboardItem === "undefined") {
+    copyToClipboard(fallback);
     return;
   }
 
@@ -195,7 +208,7 @@ export function copyValue(text: string, sniffed: SniffedValue | null, hidden: st
       // Anything from a webview that won't take an image to a file we couldn't decode. The
       // encoded text is always there to fall back on.
       console.error("Failed to copy image, copying text instead", err);
-      copyToClipboard(hidden);
+      copyToClipboard(fallback);
     });
 }