diff --git a/lib/check.ml b/lib/check.ml
index 6d06c7cd..278c614c 100644
--- a/lib/check.ml
+++ b/lib/check.ml
@@ -1991,6 +1991,12 @@ let mk loc ty e : Tast.expr = { Tast.e; ty; loc }
 
 let unit_at loc = mk loc Types.Unit Tast.Unit
 
+(* The compiler temp an [and] leaves in its else arm; see [check_if]. *)
+let and_sentinel (x : Ast.expr) =
+  match x.Ast.e with
+  | Ast.Var n -> String.length n > 4 && String.sub n 0 4 = "and~"
+  | _ -> false
+
 (* Integer arithmetic over literals alone, folded. Unlike [const_int] no name
    is read: a defconst has a type of its own, and only an untyped constant may
    stand at a type variable. *)
@@ -2015,6 +2021,10 @@ let rec literal_arith (e : Ast.expr) : int64 option =
       (literal_arith x) (y :: rest)
   | _ -> None
 
+(* A value with no type until one is asked of it: a literal, or arithmetic
+   over literals alone. *)
+let lone_literal (e : Ast.expr) = is_literal e || literal_arith e <> None
+
 
 (* The environment for a lifted body, built once its own body has been checked
    and [caught] is therefore final. spec-memory.md's case 2, and the whole of
@@ -5102,6 +5112,16 @@ and check_if ctx ?(tail = false) ?want loc c t e =
        no value on the missing side. `when` desugars to this. *)
     let t = branch ctx (fun () -> in_tail (fun () -> check ctx t)) in
     expect ctx loc ~want (mk loc Types.Unit (Tast.If (c, t, unit_at loc)))
+  | Some e when want = None && lone_literal t && not (lone_literal e)
+                && not (and_sentinel e) ->
+    (* A literal has no type of its own until something asks, so with no
+       expectation the other arm decides: [(if c 4000000 n)] over an i64 [n]
+       is an i64, as [(+ 4000000 n)] is. *)
+    let e = branch ctx (fun () -> in_tail (fun () -> check ctx e)) in
+    let twant = if e.Tast.ty = Types.Never then None else Some e.Tast.ty in
+    let t = branch ctx (fun () -> in_tail (fun () -> check ctx ?want:twant t)) in
+    let ty = if e.Tast.ty = Types.Never then t.Tast.ty else e.Tast.ty in
+    mk loc ty (Tast.If (c, t, e))
   | Some e ->
     let t = branch ctx (fun () -> in_tail (fun () -> check ctx ?want t)) in
     (* With no expectation the then-branch supplies one for the else-branch,
@@ -5125,12 +5145,6 @@ and check_if ctx ?(tail = false) ?want loc c t e =
        sentinel in the then arm, so every operand is already blamed at its own
        location; and with an expectation in hand both arms are checked against
        it rather than against each other, so nothing here runs. *)
-    let and_sentinel (x : Ast.expr) =
-      match x.Ast.e with
-      | Ast.Var n ->
-        String.length n > 4 && String.sub n 0 4 = "and~"
-      | _ -> false
-    in
     let e =
       match branch ctx (fun () -> in_tail (fun () -> check ctx ?want:ewant e)) with
       | v -> v
@@ -5840,7 +5854,7 @@ and check_match ctx ?(tail = false) ?want loc scrutinee arms =
   let want = ref want in
   let seen = Hashtbl.create 8 in
   let saw_wild = ref false in
-  let arms =
+  let resolved =
     map_lr
       (fun (a : Ast.arm) ->
          let ctor, binds = resolve_pat a in
@@ -5850,6 +5864,28 @@ and check_match ctx ?(tail = false) ?want loc scrutinee arms =
             if Hashtbl.mem seen c then
               fail a.Ast.aloc "this match has two %s arms" c;
             Hashtbl.add seen c ());
+         (a, ctor, binds))
+      arms
+  in
+  (* With nothing expected of the match, the first arm's type is every arm's —
+     unless that arm is a bare literal, which has no type until asked. So the
+     arms whose value is a literal are checked last, and take their type from
+     the others, as an [if]'s literal arm does. The order is only the order
+     they are checked in; they are put back in source order below. *)
+  let literal_arm ((a : Ast.arm), _, _) =
+    match List.rev a.Ast.body with last :: _ -> lone_literal last | [] -> false
+  in
+  let order =
+    let idx = List.mapi (fun i r -> (i, r)) resolved in
+    if !want <> None then idx
+    else
+      List.filter (fun (_, r) -> not (literal_arm r)) idx
+      @ List.filter (fun (_, r) -> literal_arm r) idx
+  in
+  let checked =
+    map_lr
+      (fun (i, ((a : Ast.arm), ctor, binds)) ->
+         i,
          branch ctx (fun () ->
            (* What each name in this arm is, in words, for the one refusal
               that needs it: a case pattern binds fields positionally, so the
@@ -5885,7 +5921,10 @@ and check_match ctx ?(tail = false) ?want loc scrutinee arms =
            if !want = None && body.Tast.ty <> Types.Never then
              want := Some body.Tast.ty;
            { Tast.acase = ctor; binds; abody = [ body ] }))
-      arms
+      order
+  in
+  let arms =
+    List.map snd (List.sort (fun (i, _) (j, _) -> compare i j) checked)
   in
   (* Exhaustiveness is refused, not defaulted. A match that silently fell
      through would have to produce a value of the match's type out of nothing,
diff --git a/test/programs/literal-arm.flan b/test/programs/literal-arm.flan
new file mode 100644
index 00000000..5459e906
--- /dev/null
+++ b/test/programs/literal-arm.flan
@@ -0,0 +1,18 @@
+;;;; A literal arm takes its type from the arm that is not a literal, in an
+;;;; if, a cond and a match alike, as a literal operand of + does.
+(defn g [c bool n i64] i64 (let [x (if c 4000000 n)] x))
+(defn h [k i32 n i64] i64
+  (let [x (cond (= k 0) 5000000000 (= k 1) 7 :else n)] x))
+(defn m [o (Option i64)] i64
+  (let [x (match o None 3 (Some v) v)] x))
+(defn f32s [c bool y f32] f32 (let [x (if c 2.5 y)] x))
+(defn main [] i32
+  (println (g true (i64 3)))
+  (println (g false (i64 9000000000)))
+  (println (h 0 (i64 1)))
+  (println (h 1 (i64 1)))
+  (println (h 2 (i64 9000000000)))
+  (println (m None))
+  (println (m (Some (i64 9000000000))))
+  (println (f32s true (f32 1.0)))
+  0)
diff --git a/test/test_acceptance.ml b/test/test_acceptance.ml
index a88787ea..8466b85e 100644
--- a/test/test_acceptance.ml
+++ b/test/test_acceptance.ml
@@ -558,6 +558,13 @@ let () =
       "programs/array-first-element.flan" first_out;
     outputs ~x86:true "an array literal's first element types the rest, x86"
       "programs/array-first-element.flan" first_out;
+    (* A literal arm takes the other arm's type. *)
+    let arm_out =
+      "4000000\n9000000000\n5000000000\n7\n9000000000\n3\n9000000000\n2.5\n" in
+    outputs "a literal arm takes the other arm's type"
+      "programs/literal-arm.flan" arm_out;
+    outputs ~x86:true "a literal arm takes the other arm's type, x86"
+      "programs/literal-arm.flan" arm_out;
     (* into. The count of pulls is the assertion a unit test cannot make: one
        pass, one call per element per stage it reaches, and no intermediate
        collection anywhere. The two show lines either side of it are the same