diff --git a/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.tests.ts b/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.tests.ts
index 8ea47e9029f..d3df0742d50 100644
--- a/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.tests.ts
+++ b/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.tests.ts
@@ -9,9 +9,13 @@
 
 import { assert } from 'chai';
 
+import { DeletionQuotientSpur, InsertionQuotientSpur } from '@keymanapp/lm-worker/test-index';
+
 import { constituentPaths } from "./constituentPaths.js";
+import { toSpurTypeSequence } from './toSpurTypeSequence.js';
 import { buildCantLinearFixture } from './buildCantLinearFixture.js';
 import { buildAlphabeticClusterFixtures } from './buildAlphabeticClusteredFixture.js';
+import { buildQuotientDocFixture } from './buildQuotientDocFixture.js';
 
 describe('constituentPaths', () => {
   it('includes a single entry array when all parents are SearchQuotientSpurs', () => {
@@ -42,4 +46,50 @@ describe('constituentPaths', () => {
       return p;
     }));
   });
+
+  describe('for the final quotient-graph doc example', () => {
+    it('handles insertion-only quotient-graph paths', () => {
+      const { sc2 } = buildQuotientDocFixture().nodes;
+
+      const sc2Constituents = constituentPaths(sc2);
+      assert.equal(sc2Constituents.length, 1);
+      sc2Constituents.forEach(s => s.forEach(p => assert.isTrue(p instanceof InsertionQuotientSpur)));
+    });
+
+    it('handles deletion-only quotient-graph paths', () => {
+      const { k2c0 } = buildQuotientDocFixture().nodes;
+
+      const k2c0Constituents = constituentPaths(k2c0);
+      assert.equal(k2c0Constituents.length, 1);
+      k2c0Constituents.forEach(s => s.forEach(p => assert.isTrue(p instanceof DeletionQuotientSpur)));
+    });
+
+    it('does not emit sequences with inserts immediately following deletes', () => {
+      const { k2c3 } = buildQuotientDocFixture().nodes;
+
+      const k2c3Constituents = constituentPaths(k2c3);
+
+      const shouldNotOccur = k2c3Constituents.find((seq) => {
+        const typeSeq = toSpurTypeSequence(seq);
+        return typeSeq.find((type, index) => {
+          return type == 'delete' && typeSeq[index+1] == 'insert';
+        });
+      });
+      assert.isNotOk(shouldNotOccur);
+    });
+
+    it('does emit sequences with deletes immediately following inserts', () => {
+      const { k2c3 } = buildQuotientDocFixture().nodes;
+
+      const k2c3Constituents = constituentPaths(k2c3);
+
+      const shouldOccur = k2c3Constituents.find((seq) => {
+        const typeSeq = toSpurTypeSequence(seq);
+        return typeSeq.find((type, index) => {
+          return type == 'insert' && typeSeq[index+1] == 'delete';
+        });
+      });
+      assert.isOk(shouldOccur);
+    });
+  });
 });
\ No newline at end of file
diff --git a/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.ts b/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.ts
index 9c01297f0ce..38325078719 100644
--- a/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.ts
+++ b/web/src/test/auto/headless/engine/predictive-text/helpers/constituentPaths.ts
@@ -8,6 +8,8 @@
  */
 
 import {
+  DeletionQuotientSpur,
+  InsertionQuotientSpur,
   SearchQuotientCluster,
   SearchQuotientNode,
   SearchQuotientRoot,
@@ -29,6 +31,28 @@ export function constituentPaths(node: SearchQuotientNode): SearchQuotientSpur[]
     const parentPaths = constituentPaths(node.parents[0]);
     let pathsToExtend = parentPaths;
 
+    if(node instanceof InsertionQuotientSpur) {
+      pathsToExtend = pathsToExtend.filter(s => {
+        const tail = s[s.length - 1];
+
+        // Deletion nodes and modules should always be ordered after those for
+        // insertion in order to avoid duplicating search paths.  (Insertions may
+        // stick to the right of a root, while deletions always process inputs; insertions
+        // may thus precede deletions.)
+        //
+        // Also, internally, insertion edges are not built after deletion (or empty) edges.
+        if(tail instanceof DeletionQuotientSpur) {
+          return false;
+        } else if(tail.insertLength == 0 && tail.leftDeleteLength == 0) {
+          // Insertions should also not appear after empty nodes; there's no net
+          // difference between inserting before and inserting after.
+          return false;
+        }
+
+        return true;
+      });
+    }
+
     if(parentPaths.length > 0) {
       return pathsToExtend.map(p => {
         p.push(node);
diff --git a/web/src/test/auto/headless/engine/predictive-text/helpers/toSpurTypeSequence.ts b/web/src/test/auto/headless/engine/predictive-text/helpers/toSpurTypeSequence.ts
new file mode 100644
index 00000000000..74c9ea182cb
--- /dev/null
+++ b/web/src/test/auto/headless/engine/predictive-text/helpers/toSpurTypeSequence.ts
@@ -0,0 +1,20 @@
+import {
+  DeletionQuotientSpur,
+  InsertionQuotientSpur,
+  SearchQuotientNode,
+  SubstitutionQuotientSpur
+} from "@keymanapp/lm-worker/test-index";
+
+export function toSpurTypeSequence(spurs: SearchQuotientNode[]): ('insert' | 'delete' | 'substitute' | 'legacy')[] {
+  return spurs.map(s => {
+    if(s instanceof InsertionQuotientSpur) {
+      return 'insert';
+    } else if(s instanceof DeletionQuotientSpur) {
+      return 'delete';
+    } else if(s instanceof SubstitutionQuotientSpur) {
+      return 'substitute';
+    } else {
+      return 'legacy';
+    }
+  })
+}
\ No newline at end of file