diff --git a/theories/proofmode/class_instances.v b/theories/proofmode/class_instances.v
index 9cec3e3081b925ce75919b84903899adadb77606..9ee852ebc03731ddf6d0edfc3398de1ef5893907 100644
--- a/theories/proofmode/class_instances.v
+++ b/theories/proofmode/class_instances.v
@@ -177,100 +177,101 @@ Proof. done. Qed.
 Global Instance make_laterN_default P : MakeLaterN n P (â–·^n P) | 100.
 Proof. done. Qed.
 
-Global Instance into_laterN_0 P : IntoLaterN 0 P P.
+Global Instance into_laterN_0 only_head P : IntoLaterN only_head 0 P P.
 Proof. done. Qed.
-Global Instance into_laterN_later n n' m' P Q lQ :
+Global Instance into_laterN_later only_head n n' m' P Q lQ :
   NatCancel n 1 n' m' →
   (** If canceling has failed (i.e. [1 = m']), we should make progress deeper
   into [P], as such, we continue with the [IntoLaterN] class, which is required
   to make progress. If canceling has succeeded, we do not need to make further
   progress, but there may still be a left-over (i.e. [n']) to cancel more deeply
   into [P], as such, we continue with [MaybeIntoLaterN]. *)
-  TCIf (TCEq 1 m') (IntoLaterN n' P Q) (MaybeIntoLaterN n' P Q) →
+  TCIf (TCEq 1 m') (IntoLaterN only_head n' P Q) (MaybeIntoLaterN only_head n' P Q) →
   MakeLaterN m' Q lQ →
-  IntoLaterN n (â–· P) lQ | 2.
+  IntoLaterN only_head n (â–· P) lQ | 2.
 Proof.
   rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel.
   move=> Hn [_ ->|->] <-;
     by rewrite -later_laterN -laterN_plus -Hn Nat.add_comm.
 Qed.
-Global Instance into_laterN_laterN n m n' m' P Q lQ :
+Global Instance into_laterN_laterN only_head n m n' m' P Q lQ :
   NatCancel n m n' m' →
-  TCIf (TCEq m m') (IntoLaterN n' P Q) (MaybeIntoLaterN n' P Q) →
+  TCIf (TCEq m m') (IntoLaterN only_head n' P Q) (MaybeIntoLaterN only_head n' P Q) →
   MakeLaterN m' Q lQ →
-  IntoLaterN n (â–·^m P) lQ | 1.
+  IntoLaterN only_head n (â–·^m P) lQ | 1.
 Proof.
   rewrite /MakeLaterN /IntoLaterN /MaybeIntoLaterN /NatCancel.
   move=> Hn [_ ->|->] <-; by rewrite -!laterN_plus -Hn Nat.add_comm.
 Qed.
 
 Global Instance into_laterN_and_l n P1 P2 Q1 Q2 :
-  IntoLaterN n P1 Q1 → MaybeIntoLaterN n P2 Q2 →
-  IntoLaterN n (P1 ∧ P2) (Q1 ∧ Q2) | 10.
+  IntoLaterN false n P1 Q1 → MaybeIntoLaterN false n P2 Q2 →
+  IntoLaterN false n (P1 ∧ P2) (Q1 ∧ Q2) | 10.
 Proof. rewrite /IntoLaterN /MaybeIntoLaterN=> -> ->. by rewrite laterN_and. Qed.
 Global Instance into_laterN_and_r n P P2 Q2 :
-  IntoLaterN n P2 Q2 → IntoLaterN n (P ∧ P2) (P ∧ Q2) | 11.
+  IntoLaterN false n P2 Q2 → IntoLaterN false n (P ∧ P2) (P ∧ Q2) | 11.
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ->. by rewrite laterN_and -(laterN_intro _ P).
 Qed.
 
 Global Instance into_later_forall {A} n (Φ Ψ : A → uPred M) :
-  (∀ x, IntoLaterN n (Φ x) (Ψ x)) → IntoLaterN n (∀ x, Φ x) (∀ x, Ψ x).
+  (∀ x, IntoLaterN false n (Φ x) (Ψ x)) →
+  IntoLaterN false n (∀ x, Φ x) (∀ x, Ψ x).
 Proof. rewrite /IntoLaterN /MaybeIntoLaterN laterN_forall=> ?. by apply forall_mono. Qed.
 Global Instance into_later_exist {A} n (Φ Ψ : A → uPred M) :
-  (∀ x, IntoLaterN n (Φ x) (Ψ x)) →
-  IntoLaterN n (∃ x, Φ x) (∃ x, Ψ x).
+  (∀ x, IntoLaterN false n (Φ x) (Ψ x)) →
+  IntoLaterN false n (∃ x, Φ x) (∃ x, Ψ x).
 Proof. rewrite /IntoLaterN /MaybeIntoLaterN -laterN_exist_2=> ?. by apply exist_mono. Qed.
 
 Global Instance into_laterN_or_l n P1 P2 Q1 Q2 :
-  IntoLaterN n P1 Q1 → MaybeIntoLaterN n P2 Q2 →
-  IntoLaterN n (P1 ∨ P2) (Q1 ∨ Q2) | 10.
+  IntoLaterN false n P1 Q1 → MaybeIntoLaterN false n P2 Q2 →
+  IntoLaterN false n (P1 ∨ P2) (Q1 ∨ Q2) | 10.
 Proof. rewrite /IntoLaterN /MaybeIntoLaterN=> -> ->. by rewrite laterN_or. Qed.
 Global Instance into_laterN_or_r n P P2 Q2 :
-  IntoLaterN n P2 Q2 →
-  IntoLaterN n (P ∨ P2) (P ∨ Q2) | 11.
+  IntoLaterN false n P2 Q2 →
+  IntoLaterN false n (P ∨ P2) (P ∨ Q2) | 11.
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ->. by rewrite laterN_or -(laterN_intro _ P).
 Qed.
 
 Global Instance into_laterN_sep_l n P1 P2 Q1 Q2 :
-  IntoLaterN n P1 Q1 → MaybeIntoLaterN n P2 Q2 →
-  IntoLaterN n (P1 ∗ P2) (Q1 ∗ Q2) | 10.
+  IntoLaterN false n P1 Q1 → MaybeIntoLaterN false n P2 Q2 →
+  IntoLaterN false n (P1 ∗ P2) (Q1 ∗ Q2) | 10.
 Proof. rewrite /IntoLaterN /MaybeIntoLaterN=> -> ->. by rewrite laterN_sep. Qed.
 Global Instance into_laterN_sep_r n P P2 Q2 :
-  IntoLaterN n P2 Q2 →
-  IntoLaterN n (P ∗ P2) (P ∗ Q2) | 11.
+  IntoLaterN false n P2 Q2 →
+  IntoLaterN false n (P ∗ P2) (P ∗ Q2) | 11.
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ->. by rewrite laterN_sep -(laterN_intro _ P).
 Qed.
 
 Global Instance into_laterN_big_sepL n {A} (Φ Ψ : nat → A → uPred M) (l: list A) :
-  (∀ x k, IntoLaterN n (Φ k x) (Ψ k x)) →
-  IntoLaterN n ([∗ list] k ↦ x ∈ l, Φ k x) ([∗ list] k ↦ x ∈ l, Ψ k x).
+  (∀ x k, IntoLaterN false n (Φ k x) (Ψ k x)) →
+  IntoLaterN false n ([∗ list] k ↦ x ∈ l, Φ k x) ([∗ list] k ↦ x ∈ l, Ψ k x).
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ?.
   rewrite big_opL_commute. by apply big_sepL_mono.
 Qed.
 Global Instance into_laterN_big_sepM n `{Countable K} {A}
     (Φ Ψ : K → A → uPred M) (m : gmap K A) :
-  (∀ x k, IntoLaterN n (Φ k x) (Ψ k x)) →
-  IntoLaterN n ([∗ map] k ↦ x ∈ m, Φ k x) ([∗ map] k ↦ x ∈ m, Ψ k x).
+  (∀ x k, IntoLaterN false n (Φ k x) (Ψ k x)) →
+  IntoLaterN false n ([∗ map] k ↦ x ∈ m, Φ k x) ([∗ map] k ↦ x ∈ m, Ψ k x).
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ?.
   rewrite big_opM_commute; by apply big_sepM_mono.
 Qed.
 Global Instance into_laterN_big_sepS n `{Countable A}
     (Φ Ψ : A → uPred M) (X : gset A) :
-  (∀ x, IntoLaterN n (Φ x) (Ψ x)) →
-  IntoLaterN n ([∗ set] x ∈ X, Φ x) ([∗ set] x ∈ X, Ψ x).
+  (∀ x, IntoLaterN false n (Φ x) (Ψ x)) →
+  IntoLaterN false n ([∗ set] x ∈ X, Φ x) ([∗ set] x ∈ X, Ψ x).
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ?.
   rewrite big_opS_commute; by apply big_sepS_mono.
 Qed.
 Global Instance into_laterN_big_sepMS n `{Countable A}
     (Φ Ψ : A → uPred M) (X : gmultiset A) :
-  (∀ x, IntoLaterN n (Φ x) (Ψ x)) →
-  IntoLaterN n ([∗ mset] x ∈ X, Φ x) ([∗ mset] x ∈ X, Ψ x).
+  (∀ x, IntoLaterN false n (Φ x) (Ψ x)) →
+  IntoLaterN false n ([∗ mset] x ∈ X, Φ x) ([∗ mset] x ∈ X, Ψ x).
 Proof.
   rewrite /IntoLaterN /MaybeIntoLaterN=> ?.
   rewrite big_opMS_commute; by apply big_sepMS_mono.
@@ -651,7 +652,7 @@ Proof.
 Qed.
 
 Global Instance frame_later p R R' P Q Q' :
-  NoBackTrack (MaybeIntoLaterN 1 R' R) →
+  NoBackTrack (MaybeIntoLaterN true 1 R' R) →
   Frame p R P Q → MakeLaterN 1 Q Q' → Frame p R' (▷ P) Q'.
 Proof.
   rewrite /Frame /MakeLaterN /MaybeIntoLaterN=>-[->] <- <-.
@@ -659,7 +660,7 @@ Proof.
 Qed.
 
 Global Instance frame_laterN p n R R' P Q Q' :
-  NoBackTrack (MaybeIntoLaterN n R' R) →
+  NoBackTrack (MaybeIntoLaterN true n R' R) →
   Frame p R P Q → MakeLaterN n Q Q' → Frame p R' (▷^n P) Q'.
 Proof.
   rewrite /Frame /MakeLaterN /MaybeIntoLaterN=>-[->] <- <-.
diff --git a/theories/proofmode/classes.v b/theories/proofmode/classes.v
index 9834e6259eb1aea8a82c7d0f376916b19cf9b165..e7585548f16689c4c83081f4b6d8a0e097aa0d00 100644
--- a/theories/proofmode/classes.v
+++ b/theories/proofmode/classes.v
@@ -99,19 +99,29 @@ IntoLaterN n P P'       MaybeIntoLaterN n Q Q'
 -------------------------------
 IntoLaterN n (P /\ Q) (P /\ Q')
 >>
+
+The Boolean [only_head] indicates whether laters should only be stripped in
+head position or also below other logical connectives. For [iNext] it should
+strip laters below other logical connectives, but this should not happen while
+framing, e.g. the following should succeed:
+
+<<
+Lemma test_iFrame_later_1 P Q : P ∗ ▷ Q -∗ ▷ (P ∗ ▷ Q).
+Proof. iIntros "H". iFrame "H". Qed.
+>>
 *)
-Class MaybeIntoLaterN {M} (n : nat) (P Q : uPred M) :=
+Class MaybeIntoLaterN {M} (only_head : bool) (n : nat) (P Q : uPred M) :=
   maybe_into_laterN : P ⊢ ▷^n Q.
-Arguments maybe_into_laterN {_} _ _ _ {_}.
-Hint Mode MaybeIntoLaterN + - - - : typeclass_instances.
+Arguments maybe_into_laterN {_} _ _ _ _ {_}.
+Hint Mode MaybeIntoLaterN + + + - - : typeclass_instances.
 
-Class IntoLaterN {M} (n : nat) (P Q : uPred M) :=
-  into_laterN :> MaybeIntoLaterN n P Q.
+Class IntoLaterN {M} (only_head : bool) (n : nat) (P Q : uPred M) :=
+  into_laterN :> MaybeIntoLaterN only_head n P Q.
 Arguments into_laterN {_} _ _ _ {_}.
-Hint Mode IntoLaterN + - ! - : typeclass_instances.
+Hint Mode IntoLaterN + + + ! - : typeclass_instances.
 
-Instance maybe_into_laterN_default {M} n (P : uPred M) :
-  MaybeIntoLaterN n P P | 1000.
+Instance maybe_into_laterN_default {M} only_head n (P : uPred M) :
+  MaybeIntoLaterN only_head n P P | 1000.
 Proof. apply laterN_intro. Qed.
 
 Class FromLaterN {M} (n : nat) (P Q : uPred M) := from_laterN : ▷^n Q ⊢ P.
diff --git a/theories/proofmode/coq_tactics.v b/theories/proofmode/coq_tactics.v
index 3eb32081bc098427d88378bc7dbeded8824d632d..077044c591d82835a00e6ca3aa78df870a1feded 100644
--- a/theories/proofmode/coq_tactics.v
+++ b/theories/proofmode/coq_tactics.v
@@ -473,7 +473,7 @@ Proof. rewrite /envs_entails. intros HΔ ?. by rewrite HΔ pure_True // left_id.
 
 (** * Later *)
 Class MaybeIntoLaterNEnv (n : nat) (Γ1 Γ2 : env (uPred M)) :=
-  into_laterN_env : env_Forall2 (MaybeIntoLaterN n) Γ1 Γ2.
+  into_laterN_env : env_Forall2 (MaybeIntoLaterN false n) Γ1 Γ2.
 Class MaybeIntoLaterNEnvs (n : nat) (Δ1 Δ2 : envs M) := {
   into_later_persistent: MaybeIntoLaterNEnv n (env_persistent Δ1) (env_persistent Δ2);
   into_later_spatial: MaybeIntoLaterNEnv n (env_spatial Δ1) (env_spatial Δ2)
@@ -482,7 +482,7 @@ Class MaybeIntoLaterNEnvs (n : nat) (Δ1 Δ2 : envs M) := {
 Global Instance into_laterN_env_nil n : MaybeIntoLaterNEnv n Enil Enil.
 Proof. constructor. Qed.
 Global Instance into_laterN_env_snoc n Γ1 Γ2 i P Q :
-  MaybeIntoLaterNEnv n Γ1 Γ2 → MaybeIntoLaterN n P Q →
+  MaybeIntoLaterNEnv n Γ1 Γ2 → MaybeIntoLaterN false n P Q →
   MaybeIntoLaterNEnv n (Esnoc Γ1 i P) (Esnoc Γ2 i Q).
 Proof. by constructor. Qed.
 
diff --git a/theories/tests/proofmode.v b/theories/tests/proofmode.v
index 910aedffc26320790c682c299c5fa5f129b9ab76..3fb0578643d560fd45d808d10ec8dfb767fc635c 100644
--- a/theories/tests/proofmode.v
+++ b/theories/tests/proofmode.v
@@ -190,6 +190,12 @@ Lemma test_iFrame_persistent (P Q : uPred M) :
   □ P -∗ Q -∗ □ (P ∗ P) ∗ (P ∧ Q ∨ Q).
 Proof. iIntros "#HP". iFrame "HP". iIntros "$". Qed.
 
+Lemma test_iFrame_later_1 P Q : P ∗ ▷ Q -∗ ▷ (P ∗ ▷ Q).
+Proof. iIntros "H". iFrame "H". Qed.
+
+Lemma test_iFrame_later_2 P Q : ▷ P ∗ ▷ Q -∗ ▷ (▷ P ∗ ▷ Q).
+Proof. iIntros "H". iFrame "H". Qed.
+
 Lemma test_iSplit_persistently P Q : □ P -∗ □ (P ∗ P).
 Proof. iIntros "#?". by iSplit. Qed.