diff --git a/CHANGELOG.md b/CHANGELOG.md
index d342498..b17ef67 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+- move the `_` fallback to a second argument typed `Exclude<T, keyof handlers>`, so it receives only the unhandled keys, and infer handler returns from short, unannotated handlers
+
 ## [0.3.0] - 2026-09-18
 
 - condensed primitive matcher factories down to 2 from formerly 4
diff --git a/backlog.tasks b/backlog.tasks
index 45ad514..d162e65 100644
--- a/backlog.tasks
+++ b/backlog.tasks
@@ -42,10 +42,10 @@ Matcher:
 ✔ Clean up: adopt the 3-overload matcher (`src/prototype-ac2.ts`) and delete the prototypes @high @done
     → `getMatcher` / `getMatcherW`, each with overloads `ExhaustiveLoose` → `Fallback` → `Handlers` (order is load-bearing)
     → fold into `src/primitive.ts` / the public API; drop `src/prototype*.ts`
-☐ `_` should receive only the unhandled `T` keys, not all of `T` @medium
-    → today `_: (shape: T) => R`; desired `_: (shape: Exclude<T, handledKeys>) => R`
-☐ An exhaustive pattern that also carries `_` must be a compile error @medium
-    → `{ a, b, _ }` for `T = "a" | "b"` is accepted today; the redundant `_` should be rejected
+✔ `_` should receive only the unhandled `T` keys, not all of `T` @medium @done
+    → the fallback is now a second argument: `(handlers, (s) => …)`, `s: Exclude<T, keyof handlers>`
+☐ A fallback for an already-exhaustive handler map must be a compile error @medium
+    → `(handlers, fallback)` with `handlers` covering all of `T` is accepted; the redundant fallback should be rejected (currying would allow the guard)
 
 Bugs:
 ✔ TS 7 LSP server logs `context canceled` on stderr at shutdown @done
diff --git a/development/library.md b/development/library.md
index 5f89e22..4f71594 100644
--- a/development/library.md
+++ b/development/library.md
@@ -3,7 +3,7 @@
 The type-level design of the public API and the limitations it carries. The
 user-facing reference is [README § API](../README.md#api).
 
-The matcher below is implemented in `src/primitive.ts` and re-exported from
+The matcher is implemented in `src/primitive.ts` and re-exported from
 `src/index.ts` as `getMatcher` / `getMatcherW`; the rest of the library is
 placeholder code.
 
@@ -11,81 +11,77 @@ placeholder code.
 
 #### Decision (2026-09)
 
-A matcher is built by a factory and applied to a pattern:
+A factory takes the universe and returns a builder; the builder takes a handler
+map and an optional fallback:
 
 ```ts
 const matcher = getMatcher<"a" | "b">()({ a: (s) => …, b: (s) => … });
+const fallback = getMatcher<"a" | "b" | "c">()({ a: (s) => … }, (s) => …);
 ```
 
-Whether the pattern is exhaustive or has a fallback is decided **at the call
-site**, by whether it carries `_` — F#'s `| _ ->`. Only the return-strictness
-axis remains, so there are two factories:
+Exhaustive or fallback is decided **at the call site**, by whether the second
+argument is present. The fallback's parameter is the remainder
+`Exclude<T, keyof Handled>`. Only the return-strictness axis remains, so there
+are two factories:
 
-- `getMatcher` — one common `R`, the best common return type of every handler;
-- `getMatcherW` — the union of every handler's return type.
+- `getMatcher` — one common `R`; the fallback must fit it;
+- `getMatcherW` — the union `PatternReturns<Handled> | R`.
 
-Both are three overloads whose order is load-bearing:
+Each factory is two overloads whose order is load-bearing:
 
-1. `ExhaustiveLoose<R, T>` = `{ [K in T]: UnaryFn<K, R> } & { _?: UnaryFn<T, R> }`
-2. `Fallback<R, T>` = `Partial<…> & { _: UnaryFn<T, R> }`
-3. `Handlers<R, T>` — the pure exhaustive shape
+1. `Handlers<T, R>` — the exhaustive form, and the contextual type of the
+   handler-map popup;
+2. `Handled extends Exact<Partial<Handlers<T, R>>, Handled>` plus
+   `Fallback<T, Handled, R>` — a partial handler map plus the fallback.
 
 #### Why
 
-- **Autocomplete reads the first overload, the error reads the last.**
-  TypeScript takes the first overload signature as the contextual type for the
-  object-literal popup, and the last for `No overload matches this call`. So
-  `ExhaustiveLoose` first yields the popup `_?, a, b` (T-keys required, `_`
-  optional) while `Handlers` last yields `Property 'b' is missing`. The two can be
-  tuned independently.
-- Two factories, not four: the fallback is a pattern _shape_, not a separate API.
-- The widened return union is derived from the pattern's handler types, so it
-  needs no fourth signature.
+- **The fallback is an argument, not a property.** TypeScript fixes a property's
+  contextual type before it infers its sibling keys, so `_: (s) => …` in the
+  handler map can only see all of `T`, never `Exclude<T, keyof Handled>`. A later
+  argument is contextually typed from inference on an earlier one, so the split
+  is what makes the remainder expressible.
+- **Overload order keeps both messages.** #1 supplies the contextual type
+  (`a, b, c`); #2 accepts a partial map once a fallback is present, so its popup
+  is optional (`a?, b?, c?`). A gap without a fallback is reported against #1.
+- **`R` needs an inference site.** `R` inside the `Exact<…>` constraint is not
+  one, so `handlers: Handled & Partial<Handlers<T, R>>` re-adds it; without that
+  `R` collapses to `unknown` when the handler params are inferred.
+- **`Exact` restores the excess-property check.** TypeScript skips it for a
+  generic constraint, so without `Exact` the handler map accepts keys outside
+  `T`.
+- Two factories, not four: the fallback is an argument, not a separate API.
 
 #### Rejected
 
-- **Four factories** (exhaustive and fallback each split by return handling).
-  The exhaustive/fallback axis is expressible as one pattern type; four
-  signatures duplicate it.
-- **Union merge** — one type `Exhaustive<R,T> | (Partial<…> & { _: … })`,
-  explicit `<T>()`. Type-safe and completable, but TypeScript reports the
-  near-miss union member, so a missing key reads `Property '_' is missing`
-  instead of naming the key. Arm order does not change the report; the overload
-  split does.
-- **Overload merge with only the exhaustive arm last.** Fixes the missing-key
-  message, but a wrong `_` parameter is then reported against the exhaustive
-  arm, and `Parameters<typeof factory>` sees only one arm.
-- **Inferred universe** — `match(pattern)` with `T` taken from the keys
-  (exhaustive) or from `_`'s annotated parameter (fallback), via `NoInfer<T>` and
-  `_?: never`, split by overloads (a plain union merges inference; measured
-  `T = "_" | "a"`). No explicit `<T>`, and pipe-friendly. Rejected because: with
-  no declared universe the exhaustive popup offers only `_`; an unannotated `_`
-  widens `T` to `string | number`; and `NoInfer` leaks into the emitted `.d.ts`,
-  raising the consumer floor to TypeScript 5.4 (README promises `>= 5.0`).
-- **Conditional `RequireKeys`** — parameter
-  `P & ("_" extends keyof P ? unknown : Handlers<R, T>)`. Gives the good
-  missing-key message, but `keyof P` counts _optional_ keys: a widened value
-  whose declared type has `_?:` bypasses the completeness check. Demanding a
-  required `_` instead rejects that case but breaks `P` inference — `P` falls back
-  to its constraint and partial literals then demand every key. Typos also need a
-  `NoExtra` guard, whose message degrades to `not assignable to never`.
-- **Cases-first curried** — `match(["a", "b"])({ a: …, b: … })`. Completion works
-  for exhaustive patterns, and the array is a single source of truth for the
-  runtime list and the union. Rejected as not pipe-friendly; it needs a runtime
-  array; and the single-call form `match(cases, pattern)` cannot infer `R` (the
-  mapped key type `K[number]` stays deferred, so `R` widens to `unknown`).
+- **Single-object `_`** (the former shape). `_` sees only all of `T`; the
+  remainder is not expressible there, and an exhaustive map plus `_` was
+  accepted.
+- **Curried handlers-first** — `(handlers)(fallback)`. `Handled` is fixed before
+  the second call, so a redundant-fallback guard would work. Rejected: two calls
+  for the common case.
+- **`this` / HKT self-reference.** `this` is post-construction (method bodies,
+  return positions); a parameter's contextual type is pre-construction.
+  `keyof this` in an interface method is the interface, not the literal.
+- **Variance / `const` type parameters / `NoInfer` / `unique symbol` brands /
+  defaulted type-param guards.** None change inference or evaluation order;
+  `in`/`out` on the handler map broke contextual typing outright. `NoInfer`
+  specifically leaks into the emitted `.d.ts`, raising the consumer floor to
+  TypeScript 5.4 (README promises `>= 5.0`).
+- **Union merge**, **overload merge with only the exhaustive arm last**,
+  **inferred universe**, **conditional `RequireKeys`**, **cases-first curried** —
+  decided against while the API was single-object; their reasons (reported
+  near-miss member, no `_` in the exhaustive popup, `NoInfer`/floor, `keyof P`
+  counts optional keys, not pipe-friendly) hold where they still apply.
 
 #### Known issue
 
-- The `_` handler receives **all** of `T`, not the unhandled subset
-  (`Exclude<T, handledKeys>`).
-- An exhaustive pattern that also carries `_` is accepted; the redundant `_`
-  should be a compile error.
-- The widened overloads carry a completeness guard
-  `keyof P extends T | "_" ? unknown : never`, because TypeScript does not apply
-  the excess-property check to a generic constraint: a generic parameter accepts
-  extra keys, a parameter typed as a concrete object type does not.
-  `PatternReturns` must be
+- A redundant fallback is accepted: when the handler map already covers `T`, the
+  fallback is still allowed. The guard would be
+  `Exclude<T, keyof Handled> extends never ? never : unknown`, but the
+  conditional is evaluated before `Handled` is inferred; currying is the only
+  encoding that fixes it (see Rejected).
+- `PatternReturns` must be
   `ReturnType<Extract<ValueOf<P>, (...args: never[]) => unknown>>` so it survives
   the closed, partly-optional `P` constraints.
 - `Parameters<typeof factory>[0]` resolves only the **last** overload, so it is
diff --git a/src/primitive.test.ts b/src/primitive.test.ts
index 6ec1899..3c445fe 100644
--- a/src/primitive.test.ts
+++ b/src/primitive.test.ts
@@ -22,11 +22,11 @@ test("getMatcher: exhaustive pattern infers one common return type", () => {
 
     // Act
     const matcher = factory({
-        a: (s): number => {
+        a: (s) => {
             expectTypeOf(s).toEqualTypeOf<"a">();
             return 1;
         },
-        b: (s): 1 | 2 => {
+        b: (s) => {
             expectTypeOf(s).toEqualTypeOf<"b">();
             return 2;
         },
@@ -69,19 +69,19 @@ test("getMatcher: dispatches on mixed string and numeric keys", () => {
 
     // Act
     const matcher = factory({
-        a: (s): number => {
+        a: (s) => {
             expectTypeOf(s).toEqualTypeOf<"a">();
             return 1;
         },
-        b: (s): 1 | 2 => {
+        b: (s) => {
             expectTypeOf(s).toEqualTypeOf<"b">();
             return 2;
         },
-        1: (n): number => {
+        1: (n) => {
             expectTypeOf(n).toEqualTypeOf<1>();
             return 10;
         },
-        2: (n): number => {
+        2: (n) => {
             expectTypeOf(n).toEqualTypeOf<2>();
             return 20;
         },
@@ -99,22 +99,24 @@ test("getMatcher: dispatches on mixed string and numeric keys", () => {
 // API: getMatcher — ❌ Exhaustive (fallback) / ✔️ ReturnsStrict
 // ============================================================================
 
-test("getMatcher: a `_` fallback makes the universe keys optional", () => {
+test("getMatcher: a `_` fallback receives the unhandled keys", () => {
     // Arrange
     const factory = getMatcher<"a" | "b" | "c">();
 
     // Act
-    const matcher = factory({
-        a: (s): 1 | 2 => {
-            expectTypeOf(s).toEqualTypeOf<"a">();
-            return 1;
+    const matcher = factory(
+        {
+            a: (s) => {
+                expectTypeOf(s).toEqualTypeOf<"a">();
+                return 1 as const;
+            },
         },
-        _: (s): 1 | 2 => {
-            // The fallback sees the whole union, not a single literal.
-            expectTypeOf(s).toEqualTypeOf<"a" | "b" | "c">();
-            return 2;
+        (s) => {
+            // The fallback sees only the keys `a` did not handle.
+            expectTypeOf(s).toEqualTypeOf<"b" | "c">();
+            return 2 as const;
         },
-    });
+    );
 
     // Assert
     expectTypeOf(matcher).toEqualTypeOf<(shape: "a" | "b" | "c") => 1 | 2>();
@@ -125,47 +127,27 @@ test("getMatcher: a `_` fallback makes the universe keys optional", () => {
     assert.equal(matcher("c"), 2);
 });
 
-test("getMatcher: a `_` fallback also accepts an exhaustive pattern", () => {
-    // Arrange
-    const factory = getMatcher<"a" | "b">();
-
-    // Act
-    const matcher = factory({
-        a: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"a">();
-            return "A";
-        },
-        b: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"b">();
-            return "B";
-        },
-    });
-
-    // Assert
-    expectTypeOf(matcher).toEqualTypeOf<(shape: "a" | "b") => string>();
-    assert.equal(matcher("a"), "A");
-    assert.equal(matcher("b"), "B");
-});
-
 test("getMatcher: a `_` fallback routes mixed string and numeric gaps", () => {
     // Arrange
     const factory = getMatcher<"a" | "b" | 1 | 2>();
 
     // Act
-    const matcher = factory({
-        a: (s): string => {
-            expectTypeOf(s).toEqualTypeOf<"a">();
-            return "A";
+    const matcher = factory(
+        {
+            a: (s) => {
+                expectTypeOf(s).toEqualTypeOf<"a">();
+                return "A";
+            },
+            1: (n) => {
+                expectTypeOf(n).toEqualTypeOf<1>();
+                return "one";
+            },
         },
-        1: (n): string => {
-            expectTypeOf(n).toEqualTypeOf<1>();
-            return "one";
-        },
-        _: (s): string => {
-            expectTypeOf(s).toEqualTypeOf<"a" | "b" | 1 | 2>();
+        (s) => {
+            expectTypeOf(s).toEqualTypeOf<"b" | 2>();
             return "fallback";
         },
-    });
+    );
 
     // Assert
     expectTypeOf(matcher).toEqualTypeOf<(shape: "a" | "b" | 1 | 2) => string>();
@@ -247,17 +229,19 @@ test("getMatcherW: a `_` fallback widens gaps into the union", () => {
     const factory = getMatcherW<"x" | "y" | "z">();
 
     // Act
-    const matcher = factory({
-        x: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"x">();
-            return 1 as const;
+    const matcher = factory(
+        {
+            x: (s) => {
+                expectTypeOf(s).toEqualTypeOf<"x">();
+                return 1 as const;
+            },
         },
-        _: (s) => {
-            // The fallback sees the whole union, not a single literal.
-            expectTypeOf(s).toEqualTypeOf<"x" | "y" | "z">();
+        (s) => {
+            // The fallback sees only the keys `x` did not handle.
+            expectTypeOf(s).toEqualTypeOf<"y" | "z">();
             return "fallback" as const;
         },
-    });
+    );
 
     // Assert
     expectTypeOf(matcher).toEqualTypeOf<
@@ -275,20 +259,22 @@ test("getMatcherW: a `_` fallback widens mixed string and numeric returns", () =
     const factory = getMatcherW<"a" | "b" | 1 | 2>();
 
     // Act
-    const matcher = factory({
-        a: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"a">();
-            return "A" as const;
+    const matcher = factory(
+        {
+            a: (s) => {
+                expectTypeOf(s).toEqualTypeOf<"a">();
+                return "A" as const;
+            },
+            1: (n) => {
+                expectTypeOf(n).toEqualTypeOf<1>();
+                return 10 as const;
+            },
         },
-        1: (n) => {
-            expectTypeOf(n).toEqualTypeOf<1>();
-            return 10 as const;
-        },
-        _: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"a" | "b" | 1 | 2>();
+        (s) => {
+            expectTypeOf(s).toEqualTypeOf<"b" | 2>();
             return "fallback" as const;
         },
-    });
+    );
 
     // Assert
     // ❌ ReturnsStrict: mixed handler returns widen to their union.
@@ -301,28 +287,6 @@ test("getMatcherW: a `_` fallback widens mixed string and numeric returns", () =
     assert.equal(matcher(2), "fallback");
 });
 
-test("getMatcherW: a `_` fallback also accepts an exhaustive pattern", () => {
-    // Arrange
-    const factory = getMatcherW<"x" | "y">();
-
-    // Act
-    const matcher = factory({
-        x: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"x">();
-            return 1 as const;
-        },
-        y: (s) => {
-            expectTypeOf(s).toEqualTypeOf<"y">();
-            return "two" as const;
-        },
-    });
-
-    // Assert
-    expectTypeOf(matcher).toEqualTypeOf<(shape: "x" | "y") => 1 | "two">();
-    assert.equal(matcher("x"), 1);
-    assert.equal(matcher("y"), "two");
-});
-
 // ============================================================================
 // Factory contracts — calls that must not compile
 // ============================================================================
@@ -341,8 +305,10 @@ test("getMatcher factory rejects patterns outside its contract", () => {
         // @ts-expect-error `c` is not part of the universe `"a" | "b"`
         c: () => 3,
     });
-    // @ts-expect-error a gap without `_` is not exhaustive
+    // @ts-expect-error a gap without a `_` fallback is not exhaustive
     factory({ a: () => 1 });
+    // @ts-expect-error a `string` fallback does not fit the `number` handler
+    factory({ a: () => 1 }, () => "x");
 });
 
 test("getMatcherW factory rejects patterns outside its contract", () => {
@@ -350,16 +316,31 @@ test("getMatcherW factory rejects patterns outside its contract", () => {
     const factory = getMatcherW<"x" | "y">();
 
     // Act / Assert — the calls below must not compile
-    // @ts-expect-error `z` is not part of the universe `"x" | "y"`
     factory({
         x: () => 1 as const,
         y: () => 2 as const,
+        // @ts-expect-error `z` is not part of the universe `"x" | "y"`
         z: () => 3 as const,
     });
-    // @ts-expect-error a gap without `_` is not exhaustive
+    // @ts-expect-error a gap without a `_` fallback is not exhaustive
     factory({ x: () => 1 as const });
 });
 
+// ============================================================================
+// Dispatch — runtime behavior
+// ============================================================================
+
+test("getMatcher: an unhandled shape throws without a fallback", () => {
+    // Arrange — an open universe types its handler map as an index signature,
+    // so the type system cannot prove the runtime map is exhaustive.
+    const handlers: Record<string, () => number> = { a: () => 1 };
+    const matcher = getMatcher<string>()(handlers);
+
+    // Act / Assert
+    assert.equal(matcher("a"), 1);
+    assert.throws(() => matcher("b"), /Unhandled shape: b/);
+});
+
 // ============================================================================
 // Autocomplete — the language server is the oracle, not the type system
 // ============================================================================
@@ -374,11 +355,19 @@ const UNIVERSE = `"a" | "b" | "c"`;
 
 // One session per probe: the tests share no language-server state (open
 // documents, project membership), so they pass in any order.
-const labelsFor = (
-    name: string,
-    factory: "getMatcher" | "getMatcherW",
-    body: string,
-): Promise<readonly string[]> => {
+interface LabelsProbe {
+    readonly name: string;
+    readonly factory: "getMatcher" | "getMatcherW";
+    readonly body: string;
+    readonly tail?: string;
+}
+
+const labelsFor = ({
+    name,
+    factory,
+    body,
+    tail = "",
+}: LabelsProbe): Promise<readonly string[]> => {
     const session = new LspSession(REPO_ROOT);
     const target: CompletionTarget = {
         file: `src/__autocomplete_${name}.ts`,
@@ -386,7 +375,7 @@ const labelsFor = (
             `import { ${factory} } from "./index.ts";`,
             `const m = ${factory}<${UNIVERSE}>()({`,
             body,
-            "});",
+            `}${tail});`,
             "",
         ].join("\n"),
     };
@@ -396,16 +385,20 @@ const labelsFor = (
         .finally(() => session.close());
 };
 
-test("autocomplete: an exhaustive pattern requires the universe, `_` optional", () => {
+test("autocomplete: an exhaustive pattern requires the universe", () => {
     // Arrange
     const name = "getMatcher_fresh";
 
     // Act
-    const labels = labelsFor(name, "getMatcher", "    /*COMPLETE*/");
+    const labels = labelsFor({
+        name,
+        factory: "getMatcher",
+        body: "    /*COMPLETE*/",
+    });
 
     // Assert
     return labels.then((result) => {
-        assert.deepEqual([...result], ["_?", "a", "b", "c"]);
+        assert.deepEqual([...result], ["a", "b", "c"]);
     });
 });
 
@@ -414,28 +407,29 @@ test("autocomplete: handled keys drop out of the popup", () => {
     const name = "getMatcher_after_key";
 
     // Act
-    const labels = labelsFor(
+    const labels = labelsFor({
         name,
-        "getMatcher",
-        "    a: () => 1,\n    /*COMPLETE*/",
-    );
+        factory: "getMatcher",
+        body: "    a: () => 1,\n    /*COMPLETE*/",
+    });
 
     // Assert
     return labels.then((result) => {
-        assert.deepEqual([...result], ["_?", "b", "c"]);
+        assert.deepEqual([...result], ["b", "c"]);
     });
 });
 
-test("autocomplete: `_` makes the remaining keys optional", () => {
+test("autocomplete: a fallback makes the remaining keys optional", () => {
     // Arrange
-    const name = "getMatcher_after_fallback";
+    const name = "getMatcher_with_fallback";
 
     // Act
-    const labels = labelsFor(
+    const labels = labelsFor({
         name,
-        "getMatcher",
-        "    _: () => 0,\n    /*COMPLETE*/",
-    );
+        factory: "getMatcher",
+        body: "    /*COMPLETE*/",
+        tail: ", () => 0",
+    });
 
     // Assert
     return labels.then((result) => {
@@ -443,15 +437,55 @@ test("autocomplete: `_` makes the remaining keys optional", () => {
     });
 });
 
+test("autocomplete: with a fallback, handled keys stay optional", () => {
+    // Arrange
+    const name = "getMatcher_with_fallback_after_key";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getMatcher",
+        body: "    a: () => 1,\n    /*COMPLETE*/",
+        tail: ", () => 0",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["b?", "c?"]);
+    });
+});
+
 test("autocomplete: `getMatcherW` offers the same popup as `getMatcher`", () => {
     // Arrange
     const name = "getMatcherW_fresh";
 
     // Act
-    const labels = labelsFor(name, "getMatcherW", "    /*COMPLETE*/");
+    const labels = labelsFor({
+        name,
+        factory: "getMatcherW",
+        body: "    /*COMPLETE*/",
+    });
 
     // Assert
     return labels.then((result) => {
-        assert.deepEqual([...result], ["_?", "a", "b", "c"]);
+        assert.deepEqual([...result], ["a", "b", "c"]);
+    });
+});
+
+test("autocomplete: `getMatcherW` also offers optional keys with a fallback", () => {
+    // Arrange
+    const name = "getMatcherW_with_fallback";
+
+    // Act
+    const labels = labelsFor({
+        name,
+        factory: "getMatcherW",
+        body: "    /*COMPLETE*/",
+        tail: ", () => 0",
+    });
+
+    // Assert
+    return labels.then((result) => {
+        assert.deepEqual([...result], ["a?", "b?", "c?"]);
     });
 });
diff --git a/src/primitive.ts b/src/primitive.ts
index 7c13a32..74f6c34 100644
--- a/src/primitive.ts
+++ b/src/primitive.ts
@@ -1,4 +1,4 @@
-import type { ValueOf } from "type-fest";
+import type { Exact, ValueOf } from "type-fest";
 
 type UnaryFn<T, R> = (shape: T) => R;
 
@@ -8,54 +8,66 @@ type PatternReturns<P> = ReturnType<
     Extract<ValueOf<P>, (...args: never[]) => unknown>
 >;
 
-type Handlers<R, T extends string | number> = { [K in T]: UnaryFn<K, R> };
+type Handlers<T extends string | number, R> = { [K in T]: UnaryFn<K, R> };
 
-// Fallback form: `_` is a required key, the T-keys are optional.
-type Fallback<R, T extends string | number> = Partial<Handlers<R, T>> & {
-    _: UnaryFn<T, R>;
-};
+// The fallback is a *second argument*, not a property of the handler map,
+// because its parameter is the remainder `Exclude<T, keyof Handled>` and TypeScript
+// fixes a property's contextual type before it infers its sibling keys. A later
+// argument, by contrast, is contextually typed from inference on an earlier
+// one, so the split is what makes the remainder expressible at all.
+// See development/library.md.
+type Fallback<T extends string | number, Handled, R> = UnaryFn<
+    Exclude<T, keyof Handled>,
+    R
+>;
 
-// Completion form: T-keys required, `_` optional. Overload #1, because
-// TypeScript takes the *first* overload as the contextual type for the popup.
-type ExhaustiveLoose<R, T extends string | number> = Handlers<R, T> & {
-    _?: UnaryFn<T, R>;
-};
+// TypeScript does not apply the excess-property check to a generic constraint,
+// so `Exact` restores it for the generic forms: a handler map can otherwise
+// carry keys outside `T`.
 
 // oxlint-disable typescript/unified-signatures
 // Strict returns: one common `R`. Overload order is load-bearing:
-//   #1 ExhaustiveLoose -> autocomplete `_?, a, b`
-//   #2 Fallback        -> accepts a partial pattern
-//   #3 Handlers (last) -> "Property 'b' is missing" is the reported error
+//   #1 Handlers (first) -> the exhaustive form and the autocomplete popup
+//   #2 Fallback (last)  -> accepts a partial handler map plus a fallback
 interface MatcherStrict<T extends string | number> {
-    <R>(pattern: ExhaustiveLoose<R, T>): UnaryFn<T, R>;
-    <R>(pattern: Fallback<R, T>): UnaryFn<T, R>;
-    <R>(pattern: Handlers<R, T>): UnaryFn<T, R>;
+    <R>(handlers: Handlers<T, R>): UnaryFn<T, R>;
+    <R, Handled extends Exact<Partial<Handlers<T, R>>, Handled>>(
+        handlers: Handled & Partial<Handlers<T, R>>,
+        fallback: Fallback<T, Handled, R>,
+    ): UnaryFn<T, R>;
 }
 // oxlint-enable typescript/unified-signatures
 
 // Widened returns: the union of every handler's return type. `P` is inferred
-// from the whole parameter, whose closed constraint supplies the
-// contextual/autocomplete type; the `keyof P` guard appended to each overload
-// rejects keys outside `T`/`_`.
+// from the whole handler map, whose closed constraint supplies the
+// contextual/autocomplete type.
+// oxlint-disable typescript/unified-signatures
 interface MatcherWidening<T extends string | number> {
-    <P extends ExhaustiveLoose<unknown, T>>(
-        pattern: P & (keyof P extends T | "_" ? unknown : never),
-    ): UnaryFn<T, PatternReturns<P>>;
-    <P extends Fallback<unknown, T>>(
-        pattern: P & (keyof P extends T | "_" ? unknown : never),
-    ): UnaryFn<T, PatternReturns<P>>;
-    <P extends Handlers<unknown, T>>(
-        pattern: P & (keyof P extends T | "_" ? unknown : never),
+    <P extends Exact<Handlers<T, unknown>, P>>(
+        handlers: P,
     ): UnaryFn<T, PatternReturns<P>>;
+    <R, Handled extends Exact<Partial<Handlers<T, unknown>>, Handled>>(
+        handlers: Handled,
+        fallback: Fallback<T, Handled, R>,
+    ): UnaryFn<T, PatternReturns<Handled> | R>;
 }
+// oxlint-enable typescript/unified-signatures
 
 type HandlerMap = Record<string | number, UnaryFn<never, unknown> | undefined>;
 
 const dispatch =
-    (pattern: HandlerMap) =>
+    (handlers: HandlerMap, fallback?: UnaryFn<never, unknown>) =>
     (shape: string | number): unknown =>
-        // oxlint-disable-next-line typescript/no-non-null-assertion typescript/no-unsafe-type-assertion
-        (pattern[shape] ?? pattern["_"]!)(shape as never);
+        (
+            handlers[shape] ??
+            fallback ??
+            (() => {
+                throw new Error(`Unhandled shape: ${shape}`);
+            })
+        )(
+            // oxlint-disable-next-line typescript/no-unsafe-type-assertion
+            shape as never,
+        );
 
 export const getMatcher = <T extends string | number>(): MatcherStrict<T> =>
     dispatch;