diff --git a/src/Lean/Meta/AppBuilder.lean b/src/Lean/Meta/AppBuilder.lean
index b6ad609875..b08017a056 100644
--- a/src/Lean/Meta/AppBuilder.lean
+++ b/src/Lean/Meta/AppBuilder.lean
@@ -440,6 +440,18 @@ def mkFunExt (h : Expr) : MetaM Expr :=
 def mkPropExt (h : Expr) : MetaM Expr :=
   mkAppM ``propext #[h]
 
+/-- Return `let_congr h₁ h₂` -/
+def mkLetCongr (h₁ h₂ : Expr) : MetaM Expr :=
+  mkAppM ``let_congr #[h₁, h₂]
+
+/-- Return `let_val_congr b h` -/
+def mkLetValCongr (b h : Expr) : MetaM Expr :=
+  mkAppM ``let_val_congr #[b, h]
+
+/-- Return `let_body_congr a h` -/
+def mkLetBodyCongr (a h : Expr) : MetaM Expr :=
+  mkAppM ``let_body_congr #[a, h]
+
 /-- Return `of_eq_true h` -/
 def mkOfEqTrue (h : Expr) : MetaM Expr :=
   mkAppM ``of_eq_true #[h]
diff --git a/src/Lean/Meta/Tactic/Simp/Main.lean b/src/Lean/Meta/Tactic/Simp/Main.lean
index 8ffdc1092c..0b155daf4c 100644
--- a/src/Lean/Meta/Tactic/Simp/Main.lean
+++ b/src/Lean/Meta/Tactic/Simp/Main.lean
@@ -323,13 +323,39 @@ where
       return { expr := (← dsimp e) }
 
   simpLet (e : Expr) : M Result := do
-    if (← getConfig).zeta then
-      match e with
-      | Expr.letE _ _ v b _ => return { expr := b.instantiate1 v }
-      | _ => unreachable!
-    else
-      -- TODO: simplify nondependent let-decls
-      return { expr := (← dsimp e) }
+    match e with
+    | Expr.letE n t v b _ =>
+      if (← getConfig).zeta then
+        return { expr := b.instantiate1 v }
+      else
+        withLocalDeclD n t fun x => do
+          let bx := b.instantiate1 x
+          /- The following step is potentially very expensive when we have many nested let-decls.
+             TODO: handle a block of nested let decls in a single pass if this becomes a performance problem. -/
+          if (← isTypeCorrect bx) then
+            let bxType ← whnf (← inferType bx)
+            let rbx ← simp bx
+            let hb? ← match rbx.proof? with
+              | none => pure none
+              | some h => pure (some (← mkLambdaFVars #[x] h))
+            if (← dependsOn bxType x.fvarId!) then
+              /- The type of the body depends on `x`. So, we use `let_body_congr` -/
+              let v' ← dsimp v
+              let e' := mkLet n t v' (← abstract rbx.expr #[x])
+              match hb? with
+              | none => return { expr := e' }
+              | some h => return { expr := e', proof? := some (← mkLetBodyCongr v' h) }
+            else
+              /- The type of the body does not depend on `x`. So, we use `let_congr` -/
+              let rv ← simp v
+              let e' := mkLet n t rv.expr (← abstract rbx.expr #[x])
+              match rv.proof?, hb? with
+              | none,   none   => return { expr := e' }
+              | some h, none   => return { expr := e', proof? := some (← mkLetValCongr (← mkLambdaFVars #[x] rbx.expr) h) }
+              | _,      some h => return { expr := e', proof? := some (← mkLetCongr (← rv.getProof) h) }
+          else
+            return { expr := (← dsimp e) }
+    | _ => unreachable!
 
   cacheResult (cfg : Config) (r : Result) : M Result := do
     if cfg.memoize then
diff --git a/tests/lean/simpZetaFalse.lean b/tests/lean/simpZetaFalse.lean
new file mode 100644
index 0000000000..da973bcc5f
--- /dev/null
+++ b/tests/lean/simpZetaFalse.lean
@@ -0,0 +1,28 @@
+constant f : Nat → Nat
+axiom f_eq (x : Nat) : f (f x) = x
+
+theorem ex1 (x : Nat) (h : f (f x) = x) : (let y := x*x; if f (f x) = x then 1 else y + 1) = 1 := by
+  simp (config := { zeta := false }) only [h]
+  traceState
+  simp
+
+#print ex1 -- uses let_congr
+
+theorem ex2 (x z : Nat) (h : f (f x) = x) (h' : z = x) : (let y := f (f x); y) = z := by
+  simp (config := { zeta := false }) only [h]
+  traceState
+  simp [h']
+
+#print ex2 -- uses let_val_congr
+
+theorem ex3 (x z : Nat) : (let α := Nat; (fun x : α => 0 + x)) = id := by
+  simp (config := { zeta := false })
+  traceState -- should not simplify let body since `fun α : Nat => fun x : α => 0 + x` is not type correct
+  simp [id]
+
+theorem ex4 (p : Prop) (h : p) : (let n := 10; fun x : { z : Nat // z < n } => x = x) = fun z => p := by
+  simp (config := { zeta := false })
+  traceState
+  simp [h]
+
+#print ex4 -- uses let_body_congr
diff --git a/tests/lean/simpZetaFalse.lean.expected.out b/tests/lean/simpZetaFalse.lean.expected.out
new file mode 100644
index 0000000000..2fa03ad295
--- /dev/null
+++ b/tests/lean/simpZetaFalse.lean.expected.out
@@ -0,0 +1,52 @@
+x : Nat
+h : f (f x) = x
+⊢ (let y := x * x;
+    if True then 1 else y + 1) =
+    1
+theorem ex1 : ∀ (x : Nat),
+  f (f x) = x →
+    (let y := x * x;
+      if f (f x) = x then 1 else y + 1) =
+      1 :=
+fun x h =>
+  Eq.mpr
+    (congrFun
+      (congrArg Eq
+        (let_congr (Eq.refl (x * x))
+          fun y =>
+            ite_congr (Eq.trans (congrFun (congrArg Eq h) x) (eq_self x)) (fun a => Eq.refl 1)
+              fun a => Eq.refl (y + 1)))
+      1)
+    (of_eq_true (Eq.trans (congrFun (congrArg Eq (ite_true 1 (x * x + 1))) 1) (eq_true_of_decide (Eq.refl true))))
+x z : Nat
+h : f (f x) = x
+h' : z = x
+⊢ (let y := x;
+    y) =
+    z
+theorem ex2 : ∀ (x z : Nat),
+  f (f x) = x →
+    z = x →
+      (let y := f (f x);
+        y) =
+        z :=
+fun x z h h' =>
+  Eq.mpr (congrFun (congrArg Eq (let_val_congr (fun y => y) h)) z)
+    (of_eq_true (Eq.trans (congrArg (Eq x) h') (eq_self x)))
+x z : Nat
+⊢ (let α := Nat;
+    fun x => 0 + x) =
+    id
+p : Prop
+h : p
+⊢ (let n := 10;
+    fun x => True) =
+    fun z => p
+theorem ex4 : ∀ (p : Prop),
+  p →
+    (let n := 10;
+      fun x => x = x) =
+      fun z => p :=
+fun p h =>
+  Eq.mpr (congrFun (congrArg Eq (let_body_congr 10 fun n => funext fun x => eq_self x)) fun z => p)
+    (of_eq_true (Eq.trans (congrArg (Eq fun x => True) (funext fun z => eq_true h)) (eq_self fun x => True)))