diff --git a/src/Lean/Compiler/LCNF/FixedParams.lean b/src/Lean/Compiler/LCNF/FixedParams.lean
index 490e1dcbc0..a8b35bb3d6 100644
--- a/src/Lean/Compiler/LCNF/FixedParams.lean
+++ b/src/Lean/Compiler/LCNF/FixedParams.lean
@@ -104,10 +104,31 @@ partial def evalLetValue (e : LetValue) : FixParamM Unit := do
   | .const declName _ args => evalApp declName args
   | _ => return ()
 
+partial def isEquivalentFunDecl? (decl : FunDecl) : FixParamM (Option Nat) := do
+  let .let { fvarId, value := (.fvar funFvarId args), .. } k := decl.value | return none
+  if args.size != decl.params.size then return none
+  let .return retFVarId := k | return none
+  if retFVarId != fvarId then return none
+  let some (.val funIdx) := (← read).assignment.find? funFvarId | return none
+  for h : i in [:decl.params.size] do
+    let param := decl.params[i]
+    -- TODO: Eliminate this dynamic bounds check.
+    let arg := args[i]!
+    if arg != .fvar param.fvarId && arg != .erased then return none
+  return some funIdx
+
 partial def evalCode (code : Code) : FixParamM Unit := do
   match code with
   | .let decl k => evalLetValue decl.value; evalCode k
-  | .fun decl k | .jp decl k => evalCode decl.value; evalCode k
+  | .fun decl k =>
+    if let some paramIdx ← isEquivalentFunDecl? decl then
+      withReader (fun ctx =>
+                    { ctx with assignment := ctx.assignment.insert decl.fvarId (.val paramIdx) })
+        do evalCode k
+    else
+      evalCode decl.value
+      evalCode k
+  | .jp decl k => evalCode decl.value; evalCode k
   | .cases c => c.alts.forM fun alt => evalCode alt.getCode
   | .unreach .. | .jmp .. | .return .. => return ()
 
diff --git a/tests/lean/run/specFixedHOParamModuloErased.lean b/tests/lean/run/specFixedHOParamModuloErased.lean
new file mode 100644
index 0000000000..dc902da5c0
--- /dev/null
+++ b/tests/lean/run/specFixedHOParamModuloErased.lean
@@ -0,0 +1,10 @@
+/--
+trace: [Compiler.specialize.info] pmap [true, true, false, true]
+[Compiler.specialize.info] pmap [N, N, O, H]
+-/
+#guard_msgs in
+set_option trace.Compiler.specialize.info true in
+@[specialize]
+def pmap : (l : List α) → (f : (a : α) → a ∈ l → β) → List β
+  | [], _ => []
+  | a :: l, f => f a List.mem_cons_self :: pmap l (fun a h => f a (List.mem_cons_of_mem _ h))