diff --git a/src/editor/inspector/edgeSection.ts b/src/editor/inspector/edgeSection.ts
index 0522545b..ad6b979a 100644
--- a/src/editor/inspector/edgeSection.ts
+++ b/src/editor/inspector/edgeSection.ts
@@ -3,10 +3,10 @@ import { findNode, type GraphEdge, isStateNode, resolveDef, stateName } from '..
 import { graphLookup } from '../../core/model/graphLookup';
 import { findGraphAsset, type Project } from '../../core/model/Project';
 import { textOf } from '../../core/model/Properties';
-import { Button, Label } from '../../ui';
-import { hideLinks, linkNoun, removeGraphSelection } from '../actions';
+import { Label } from '../../ui';
+import { linkNoun } from '../actions';
 import { createFieldRow, labelledRow } from './fieldFactory';
-import { addGap, addNote, addTitle, type InspectorHost } from './host';
+import { addNote, addTitle, type InspectorHost } from './host';
 
 const NAME_KEY = 'transition-name';
 
@@ -64,7 +64,10 @@ export function edgeSignature(
   return d ? [d.transition, d.from, d.output, d.to, d.input, d.type].join('|') : 'missing';
 }
 
-/** One link: where it comes from and goes to. Several: how many, and the way to delete them. */
+/**
+ * One link: where it comes from and goes to. Several: how many. Hiding and deleting live in the
+ * right-click menu of the line, not here.
+ */
 export function buildEdgeSection(
   host: InspectorHost,
   assetId: string,
@@ -72,18 +75,9 @@ export function buildEdgeSection(
   edgeIds: readonly string[],
 ): void {
   const noun = linkNoun(host.state, assetId);
-  const remove = (label: string) =>
-    host.body.add(
-      new Button(label, {
-        variant: 'danger',
-        onClick: () => removeGraphSelection(host.state, assetId, [], [], edgeIds),
-      }),
-    );
   if (edgeIds.length > 1) {
     addTitle(host, `${edgeIds.length} ${noun.toUpperCase()}S`);
     addNote(host, 'Delete removes all of them in one step.');
-    addGap(host);
-    remove(`Delete ${edgeIds.length} ${noun}s`);
     return;
   }
   const d = describeEdge(host.state.project, assetId, edgeId);
@@ -109,10 +103,6 @@ export function buildEdgeSection(
     fact('Input', d.input);
     fact('Type', d.type);
   }
-  addGap(host);
-  if (!d.transition)
-    host.body.add(new Button('Hide link', { onClick: () => hideLinks(host.state, assetId, [edgeId]) }));
-  remove(`Delete ${noun}`);
 }
 
 /** Pushes the current name into its row. False when the link is gone (rebuild). */
diff --git a/tools/e2e/06-graph.mjs b/tools/e2e/06-graph.mjs
index 1914b7ce..fe20ee82 100644
--- a/tools/e2e/06-graph.mjs
+++ b/tools/e2e/06-graph.mjs
@@ -2009,7 +2009,9 @@ export async function graph(t) {
         s.selection.edgeId === 'lk-e1' &&
         same(await drawn(), ['lk-e1']) &&
         Boolean(await find('LINK')) &&
-        Boolean(await find('Delete link')),
+        // Hiding and deleting live in the line's menu alone; the inspector only describes.
+        !(await find('Hide link')) &&
+        !(await find('Delete link')),
       JSON.stringify({ selection: s.selection, drawn: await drawn() }),
     );
     await press('Delete');
@@ -2042,8 +2044,7 @@ export async function graph(t) {
     await click(one.x, two.y + 60);
     await click(two.x, two.y, 'right');
     const offered = Boolean(await find('Hide link'));
-    // The inspector shows a button of the same name; the menu's entry is the one drawn last.
-    const entry = await locate('Delete link', true);
+    const entry = await locate('Delete link');
     await click(entry.x, entry.y);
     const afterMenu = await edges();
     await undo();
diff --git a/tools/e2e/26-state-machine.mjs b/tools/e2e/26-state-machine.mjs
index 02283db2..a131c47b 100644
--- a/tools/e2e/26-state-machine.mjs
+++ b/tools/e2e/26-state-machine.mjs
@@ -374,12 +374,12 @@ export async function stateMachine(t) {
   const arrowSelection = (await state()).selection;
   await shot('05f-picked');
   check(
-    'clicking a transition picks it: the inspector shows it with its name and the way to delete it',
+    'clicking a transition picks it: the inspector shows it with its name and no button of its own',
     arrowSelection?.kind === 'edge' &&
       arrowSelection.edgeId === alarm?.id &&
       JSON.stringify(await json('__gm.stateMachine.pickedEdges()')) === JSON.stringify([alarm?.id]) &&
       (await has('TRANSITION')) &&
-      (await has('Delete transition')),
+      !(await has('Delete transition')),
     JSON.stringify({ arrowSelection, drawn: await json('__gm.stateMachine.pickedEdges()') }),
   );
   await press('Delete');