diff --git a/src/Lean/Meta/Tactic/Simp/Main.lean b/src/Lean/Meta/Tactic/Simp/Main.lean
index 48a14c8f73..679d224ce5 100644
--- a/src/Lean/Meta/Tactic/Simp/Main.lean
+++ b/src/Lean/Meta/Tactic/Simp/Main.lean
@@ -487,6 +487,14 @@ where
     else
       congrDefault e
 
+  simpMatch? (e : Expr) : M (Option Result) := do
+    let .const declName _ := e.getAppFn
+      | return none
+    if let some info ← getMatcherInfo? declName then
+      simpMatchDiscrs? simp dsimp info e
+    else
+      return none
+
   simpApp (e : Expr) : M Result := do
     let e' ← reduceStep e
     if e' != e then
@@ -494,6 +502,8 @@ where
     else if isOfNatNatLit e' then
       -- Recall that we expand "orphan" kernel nat literals `n` into `ofNat n`
       return { expr := e' }
+    else if let some r ← simpMatch? e' then
+      simpLoop r
     else
       congr e'
 
diff --git a/src/Lean/Meta/Tactic/Simp/Types.lean b/src/Lean/Meta/Tactic/Simp/Types.lean
index 849b7dc268..7d26120e1d 100644
--- a/src/Lean/Meta/Tactic/Simp/Types.lean
+++ b/src/Lean/Meta/Tactic/Simp/Types.lean
@@ -190,6 +190,46 @@ The resulting proof is built using `congr` and `congrFun` theorems.
       i := i + 1
     return r
 
+/--
+Given a match-application `e` with `MatcherInfo` `info`, return `some result`
+if at least of one of the discriminants has been simplified.
+-/
+@[specialize] def simpMatchDiscrs?
+    [Monad m] [MonadLiftT MetaM m] [MonadLiftT IO m] [MonadRef m] [MonadOptions m] [MonadTrace m] [AddMessageContext m]
+    (simp : Expr → m Result)
+    (dsimp : Expr → m Expr)
+    (info : MatcherInfo) (e : Expr) : m (Option Result) := do
+  let numArgs := e.getAppNumArgs
+  if numArgs < info.arity then
+    return none
+  let prefixSize := info.numParams + 1 /- motive -/
+  let n     := numArgs - prefixSize
+  let f     := e.extractNumArgs n
+  let infos := (← getFunInfoNArgs f n).paramInfo
+  let args  := e.getAppArgsN n
+  let mut r : Result := { expr := f }
+  let mut modified := false
+  for i in [0 : info.numDiscrs] do
+    let arg := args[i]!
+    if i < infos.size && !infos[i]!.hasFwdDeps then
+      let argNew ← simp arg
+      if argNew.expr != arg then modified := true
+      r ← mkCongr r argNew
+    else if (← whnfD (← inferType r.expr)).isArrow then
+      let argNew ← simp arg
+      if argNew.expr != arg then modified := true
+      r ← mkCongr r argNew
+    else
+      let argNew ← dsimp arg
+      if argNew != arg then modified := true
+      r ← mkCongrFun r argNew
+  unless modified do
+    return none
+  for i in [info.numDiscrs : args.size] do
+    let arg := args[i]!
+    r ← mkCongrFun r arg
+  return some r
+
 /--
 Helper class for generalizing `mkCongrSimp?`
 -/
diff --git a/tests/lean/run/simpMatchDiscrIssue.lean b/tests/lean/run/simpMatchDiscrIssue.lean
new file mode 100644
index 0000000000..b7cf30ef5e
--- /dev/null
+++ b/tests/lean/run/simpMatchDiscrIssue.lean
@@ -0,0 +1,24 @@
+/-!
+Test support for `match`-applications in the simplifier.
+The discriminants should be simplified before trying to apply congruence.
+In the following example, the term `g (a + <num>)` takes an
+exponential amount of time to be simplified the discriminants are not simplified,
+and the `match`-application reduced before visiting the alternatives.
+-/
+
+def myid (x : Nat) := 0 + x
+
+@[simp] theorem myid_eq : myid x = x := by simp [myid]
+
+def f (x : Nat) (y z : Nat) : Nat :=
+  match myid x with
+  | 0   => y
+  | _+1 => z
+
+def g (x : Nat) : Nat :=
+  match x with
+  | 0 => 1
+  | a+1 => f x (g a + 1) (g a)
+
+theorem ex (h : a = 1) : g (a+64) = a := by
+  simp [g, f, h]
diff --git a/tests/lean/simp_trace.lean.expected.out b/tests/lean/simp_trace.lean.expected.out
index aa380ca3af..2d4398c90b 100644
--- a/tests/lean/simp_trace.lean.expected.out
+++ b/tests/lean/simp_trace.lean.expected.out
@@ -34,7 +34,7 @@ Try this: simp (config := { unfoldPartialApp := true }) only [f1, modify, modify
         | (a, s) => (fun s => set (g s)) a s
 [Meta.Tactic.simp.rewrite] unfold getThe, getThe Nat s ==> MonadStateOf.get s
 [Meta.Tactic.simp.rewrite] unfold StateT.get, StateT.get s ==> pure (s, s)
-[Meta.Tactic.simp.rewrite] unfold StateT.set, StateT.set (g a) s ==> pure (PUnit.unit, g a)
+[Meta.Tactic.simp.rewrite] unfold StateT.set, StateT.set (g s) s ==> pure (PUnit.unit, g s)
 [Meta.Tactic.simp.rewrite] @eq_self:1000, (fun s => (PUnit.unit, g s)) = fun s => (PUnit.unit, g s) ==> True
 Try this: simp only [bla, h]
 [Meta.Tactic.simp.rewrite] unfold bla, bla x ==> match h x with