diff --git a/src/Lean/Meta/Tactic/Simp/SimpTheorems.lean b/src/Lean/Meta/Tactic/Simp/SimpTheorems.lean
index 143f226246..92df535ef2 100644
--- a/src/Lean/Meta/Tactic/Simp/SimpTheorems.lean
+++ b/src/Lean/Meta/Tactic/Simp/SimpTheorems.lean
@@ -422,7 +422,20 @@ def SimpTheorems.addDeclToUnfold (d : SimpTheorems) (declName : Name) : MetaM Si
     let mut d := d
     for eqn in eqns do
       d ← SimpTheorems.addConst d eqn
-    if hasSmartUnfoldingDecl (← getEnv) declName then
+    /-
+    Even if a function has equation theorems,
+    we also store it in the `toUnfold` set in the following two cases:
+    1- It was defined by structural recursion and has a smart-unfolding associated declaration.
+    2- It is non-recursive.
+
+    Reason: `unfoldPartialApp := true` or conditional equations may not apply.
+
+    Remark: In the future, we are planning to disable this
+    behavior unless `unfoldPartialApp := true`.
+    Moreover, users will have to use `f.eq_def` if they want to force the definition to be
+    unfolded.
+    -/
+    if hasSmartUnfoldingDecl (← getEnv) declName || !(← isRecursiveDefinition declName) then
       d := d.addDeclToUnfoldCore declName
     return d
   else
diff --git a/tests/lean/run/unfoldPartialRegression.lean b/tests/lean/run/unfoldPartialRegression.lean
new file mode 100644
index 0000000000..4e0c0d3bde
--- /dev/null
+++ b/tests/lean/run/unfoldPartialRegression.lean
@@ -0,0 +1,47 @@
+universe u
+
+class Zero (α : Type u) where
+  zero : α
+
+instance (priority := 300) Zero.toOfNat0 {α} [Zero α] : OfNat α (nat_lit 0) where
+  ofNat := ‹Zero α›.1
+
+class One (α : Type u) where
+  one : α
+
+instance (priority := 300) One.toOfNat1 {α} [One α] : OfNat α (nat_lit 1) where
+  ofNat := ‹One α›.1
+instance (priority := 200) One.ofOfNat1 {α} [OfNat α (nat_lit 1)] : One α where
+  one := 1
+
+@[match_pattern] def bit0 {α : Type u} [Add α] (a : α) : α := a + a
+
+@[match_pattern] def bit1 {α : Type u} [One α] [Add α] (a : α) : α := bit0 a + 1
+
+class AddZeroClass (M : Type u) extends Zero M, Add M where
+  zero_add : ∀ a : M, 0 + a = a
+  add_zero : ∀ a : M, a + 0 = a
+
+open AddZeroClass
+
+theorem bit0_zero {M} [AddZeroClass M] : bit0 (0 : M) = 0 :=
+  add_zero _
+
+def bit (b : Bool) : Nat → Nat :=
+  cond b bit1 bit0
+
+-- This is `Nat.bit_mod_two` from `Mathlib.Data.Nat.Bitwise`.
+-- Here it works fine:
+example (a : Bool) (x : Nat) :
+    bit a x % 2 = if a then 1 else 0 := by
+  simp (config := { unfoldPartialApp := true }) only [bit, bit1, bit0, ← Nat.mul_two, Bool.cond_eq_ite]
+  split <;> simp [Nat.add_mod]
+
+-- Now prove one more theorem
+theorem bit1_zero {M} [AddZeroClass M] [One M] : bit1 (0 : M) = 1 := by rw [bit1, bit0_zero, zero_add]
+
+-- Now try again:
+example (a : Bool) (x : Nat) :
+    bit a x % 2 = if a then 1 else 0 := by
+  simp (config := { unfoldPartialApp := true }) only [bit, bit1, bit0, ← Nat.mul_two, Bool.cond_eq_ite]
+  split <;> simp [Nat.add_mod] -- fails