diff --git a/src/tagged-union.test.ts b/src/tagged-union.test.ts
index 36a3564..bd6f4b1 100644
--- a/src/tagged-union.test.ts
+++ b/src/tagged-union.test.ts
@@ -893,10 +893,10 @@ test("getTaggedUnionMatcher: the maximum illegal tag universe is rejected", () =
 });
 
 // ============================================================================
-// Union-valued and optional discriminants
+// Property unions
 // ============================================================================
 
-test("getTaggedUnionMatcher: a union-valued property narrows per handler", () => {
+test("property union: narrows each handler", () => {
     // Arrange — one shape, not a union of variants; `color` is a union.
     interface Paint {
         readonly color: "red" | "green" | "blue";
@@ -939,7 +939,7 @@ test("getTaggedUnionMatcher: a union-valued property narrows per handler", () =>
     assert.equal(describe({ color: "blue", value: 3 }), 3);
 });
 
-test("getTaggedUnionMatcher: a fallback narrows a union-valued property", () => {
+test("property union: a fallback receives the unhandled values", () => {
     // Arrange
     interface Paint {
         color: "red" | "green" | "blue";
@@ -976,7 +976,7 @@ test("getTaggedUnionMatcher: a fallback narrows a union-valued property", () =>
     assert.equal(describe({ color: "blue", value: 3 }), 2);
 });
 
-test("getTaggedUnionMatcher: a numeric union-valued property narrows per handler", () => {
+test("property union: a numeric property narrows each handler", () => {
     // Arrange
     interface Version {
         code: 1 | 2 | 3;
@@ -1010,7 +1010,7 @@ test("getTaggedUnionMatcher: a numeric union-valued property narrows per handler
     assert.equal(describe({ code: 3, value: 30 }), 3);
 });
 
-test("getTaggedUnionMatcher: an optional discriminant narrows both handlers", () => {
+test("property union: an optional property is required for a defined tag", () => {
     // Arrange — `type?` is `"x" | undefined`; both handlers must be typed,
     // and matching `"x"` proves the key is present, so `type` becomes required.
     interface Maybe {
@@ -1041,7 +1041,7 @@ test("getTaggedUnionMatcher: an optional discriminant narrows both handlers", ()
     assert.equal(describe({ value: 2 }), 2);
 });
 
-test("getTaggedUnionMatcher: an optional discriminant fallback keeps the undefined tag", () => {
+test("property union: an optional fallback receives the undefined tag", () => {
     // Arrange
     interface Maybe {
         type?: "x";
@@ -1074,7 +1074,7 @@ test("getTaggedUnionMatcher: an optional discriminant fallback keeps the undefin
     assert.equal(describe({ value: 2 }), 2);
 });
 
-test("getTaggedUnionMatcher: explicit `undefined` stays distinct from absence", () => {
+test("property union: explicit `undefined` stays distinct from absence", () => {
     // Arrange — `type?: "x" | undefined` admits an explicit `undefined`, unlike
     // the bare optional above; the two representations must not be conflated.
     interface Explicit {
@@ -1107,7 +1107,7 @@ test("getTaggedUnionMatcher: explicit `undefined` stays distinct from absence",
     assert.equal(describe({ value: 3 }), 2);
 });
 
-test("getTaggedUnionMatcher: a union-valued member is split, not dropped", () => {
+test("property union: a union-valued member is split, not dropped", () => {
     // A member whose tag is itself a union sits beside a singleton-tag member.
     // Selecting members with `Extract<T, Record<K, V>>` keeps only the
     // singleton; the distributive narrowing must keep both sides of the
@@ -1139,7 +1139,7 @@ test("getTaggedUnionMatcher: a union-valued member is split, not dropped", () =>
     assert.equal(describe({ kind: "b", b: 3 }), 2);
 });
 
-test("getTaggedUnionMatcherW: a union-valued property widens to the union of returns", () => {
+test("property union: getTaggedUnionMatcherW widens the returns", () => {
     // Arrange
     interface Paint {
         color: "red" | "green" | "blue";
@@ -1173,7 +1173,7 @@ test("getTaggedUnionMatcherW: a union-valued property widens to the union of ret
     assert.equal(describe({ color: "blue", value: 3 }), true);
 });
 
-test("getTaggedUnionMatcher: a union-valued property still enforces its contract", () => {
+test("property union: enforces its contract", () => {
     // Arrange
     interface Paint {
         color: "red" | "green" | "blue";
@@ -1195,6 +1195,55 @@ test("getTaggedUnionMatcher: a union-valued property still enforces its contract
     factory({ red: () => 1, green: () => 2, blue: () => 3 }, () => 0);
 });
 
+test("property union: a broad value in the union is rejected", () => {
+    // Arrange — the property is a union, but not a finite union of literals: a
+    // template literal cannot be proven exhaustive.
+    interface Template {
+        kind: "a" | `x-${number}`;
+        a: number;
+    }
+
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error a template literal is not a finite literal
+    getTaggedUnionMatcher<Template>()("kind")({ a: () => 1 });
+    // @ts-expect-error the widening factory rejects broad values too
+    getTaggedUnionMatcherW<Template>()("kind")({ a: () => 1 });
+});
+
+test("property union: a value/stringification collision is rejected", () => {
+    // Arrange — one property holding both a value and its stringification; both
+    // would key the same handler.
+    interface BooleanColliding {
+        kind: "true" | true;
+        a: number;
+    }
+    interface NumericColliding {
+        kind: "1" | 1;
+        a: number;
+    }
+
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `true` collides with the string tag `"true"`
+    getTaggedUnionMatcher<BooleanColliding>()("kind")({ true: () => 1 });
+    // @ts-expect-error the number tag `1` collides with the string tag `"1"`
+    getTaggedUnionMatcher<NumericColliding>()("kind")({ "1": () => 1 });
+    // @ts-expect-error the widening factory rejects the collision too
+    getTaggedUnionMatcherW<BooleanColliding>()("kind")({ true: () => 1 });
+});
+
+test("property union: a collision is rejected beside legal members", () => {
+    // Arrange — the map is otherwise complete, so only the collision can make
+    // it invalid.
+    interface Colliding {
+        kind: "true" | true | "a";
+        a: number;
+    }
+
+    // Act / Assert — the call below must not compile
+    // @ts-expect-error `true` collides with the string tag `"true"`
+    getTaggedUnionMatcher<Colliding>()("kind")({ true: () => 1, a: () => 2 });
+});
+
 // ============================================================================
 // Dispatch — runtime behavior
 // ============================================================================
@@ -1238,6 +1287,7 @@ interface LabelsProbe {
     readonly tail?: string;
     readonly typeName?: string;
     readonly typeSource?: string;
+    readonly key?: string;
 }
 
 const labelsFor = ({
@@ -1247,6 +1297,7 @@ const labelsFor = ({
     tail = "",
     typeName = "Shape",
     typeSource = SHAPE_SOURCE,
+    key = "kind",
 }: LabelsProbe): Promise<readonly string[]> => {
     const session = new LspSession(REPO_ROOT);
     const target: CompletionTarget = {
@@ -1254,7 +1305,7 @@ const labelsFor = ({
         source: [
             `import { ${factory} } from "./index.ts";`,
             typeSource,
-            `const m = ${factory}<${typeName}>()("kind")({`,
+            `const m = ${factory}<${typeName}>()("${key}")({`,
             body,
             `}${tail});`,
             "",
@@ -1341,6 +1392,91 @@ test("autocomplete: boolean and nullish tags are offered by name", () => {
     });
 });
 
+// A single shape whose property is a union: the popup is still keyed by the
+// property's values, not by the members of a union type.
+const PALETTE_SOURCE = `interface Palette { color: "red" | "green" | "blue"; value: number }`;
+const FLAG_SOURCE = `interface Flag { kind: true | false | null | undefined; a: number }`;
+
+test("property union: autocomplete offers the property's values", () => {
+    // Arrange
+    const name = "property_union_fresh";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        typeName: "Palette",
+        typeSource: PALETTE_SOURCE,
+        key: "color",
+        body: "    /*COMPLETE*/",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["blue", "green", "red"]);
+    });
+});
+
+test("property union: autocomplete drops a handled value", () => {
+    // Arrange
+    const name = "property_union_after_key";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        typeName: "Palette",
+        typeSource: PALETTE_SOURCE,
+        key: "color",
+        body: "    red: () => 1,\n    /*COMPLETE*/",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["blue", "green"]);
+    });
+});
+
+test("property union: autocomplete makes the remaining values optional with a fallback", () => {
+    // Arrange
+    const name = "property_union_with_fallback";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        typeName: "Palette",
+        typeSource: PALETTE_SOURCE,
+        key: "color",
+        body: "    /*COMPLETE*/",
+        tail: ", () => 0",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["blue?", "green?", "red?"]);
+    });
+});
+
+test("property union: autocomplete offers boolean and nullish values by name", () => {
+    // Arrange
+    const name = "property_union_boolean_nullish";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getTaggedUnionMatcher",
+        typeName: "Flag",
+        typeSource: FLAG_SOURCE,
+        body: "    /*COMPLETE*/",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["false", "null", "true", "undefined"]);
+    });
+});
+
 // `Mixed` has two common keys, but `id`'s value is not a tag, so only `kind`
 // may serve as the discriminant.
 const MIXED_SOURCE = `type Mixed = { id: Date; kind: "a"; a: number } | { id: Date; kind: "b"; b: number };`;