diff --git a/theories/heap_lang/tactics.v b/theories/heap_lang/tactics.v
index 6cfa3e1dfe59835007d5365c6faf66b727f9f729..64401c566756b1d25956114fc47a8ffede975689 100644
--- a/theories/heap_lang/tactics.v
+++ b/theories/heap_lang/tactics.v
@@ -187,9 +187,9 @@ Definition is_atomic (e : expr) :=
   | App (Rec _ _ (Lit _)) (Lit _) => true
   | _ => false
   end.
-Lemma is_atomic_correct e : is_atomic e → StronglyAtomic (to_expr e).
+Lemma is_atomic_correct e : is_atomic e → Atomic (to_expr e).
 Proof.
-  intros He. apply ectx_language_strongly_atomic.
+  intros He. apply strongly_atomic_atomic, ectx_language_strong_atomic.
   - intros σ e' σ' ef Hstep; simpl in *. revert Hstep.
     destruct e=> //=; repeat (simplify_eq/=; case_match=>//);
       inversion 1; simplify_eq/=; rewrite ?to_of_val; eauto.
@@ -226,11 +226,11 @@ Hint Extern 10 (AsVal _) => solve_as_val : typeclass_instances.
 
 Ltac solve_atomic :=
   match goal with
-  | |- StronglyAtomic ?e =>
-     let e' := W.of_expr e in change (StronglyAtomic (W.to_expr e'));
+  | |- Atomic ?e =>
+     let e' := W.of_expr e in change (Atomic (W.to_expr e'));
      apply W.is_atomic_correct; vm_compute; exact I
   end.
-Hint Extern 10 (StronglyAtomic _) => solve_atomic : typeclass_instances.
+Hint Extern 10 (Atomic _) => solve_atomic : typeclass_instances.
 
 (** Substitution *)
 Ltac simpl_subst :=
diff --git a/theories/program_logic/ectx_language.v b/theories/program_logic/ectx_language.v
index af8b796f9036be1a2117ff1f6c3d3926cfa4ebd7..3bad0f0536732cc5f67f7bf1132aea614442a9ee 100644
--- a/theories/program_logic/ectx_language.v
+++ b/theories/program_logic/ectx_language.v
@@ -117,20 +117,20 @@ Section ectx_language.
     rewrite -not_reducible -not_head_reducible. eauto using prim_head_reducible.
   Qed.
 
-  Lemma ectx_language_atomic e :
-    (∀ σ e' σ' efs, head_step e σ e' σ' efs → irreducible e' σ') →
+  Lemma ectx_language_strong_atomic e :
+    (∀ σ e' σ' efs, head_step e σ e' σ' efs → is_Some (to_val e')) →
     sub_redexes_are_values e →
-    Atomic e.
+    StronglyAtomic e.
   Proof.
     intros Hatomic_step Hatomic_fill σ e' σ' efs [K e1' e2' -> -> Hstep].
     assert (K = empty_ectx) as -> by eauto 10 using val_stuck.
     rewrite fill_empty. eapply Hatomic_step. by rewrite fill_empty.
   Qed.
 
-  Lemma ectx_language_strongly_atomic e :
-    (∀ σ e' σ' efs, head_step e σ e' σ' efs → is_Some (to_val e')) →
-    sub_values e →
-    StronglyAtomic e.
+  Lemma ectx_language_atomic e :
+    (∀ σ e' σ' efs, head_step e σ e' σ' efs → irreducible e' σ') →
+    sub_redexes_are_values e →
+    Atomic e.
   Proof.
     intros Hatomic_step Hatomic_fill σ e' σ' efs [K e1' e2' -> -> Hstep].
     assert (K = empty_ectx) as -> by eauto 10 using val_stuck.
diff --git a/theories/program_logic/hoare.v b/theories/program_logic/hoare.v
index b3a8a4677eb5ae9ed0eea8ccf4a08efe89b609e1..953c05f6fe3d9984e908c78586ec29427c6f32c0 100644
--- a/theories/program_logic/hoare.v
+++ b/theories/program_logic/hoare.v
@@ -42,6 +42,7 @@ Notation "{{ P } } e ? {{ v , Q } }" := (ht false ⊤ P%I e%E (λ v, Q)%I)
 
 Section hoare.
 Context `{irisG Λ Σ}.
+Implicit Types p : bool.
 Implicit Types P Q : iProp Σ.
 Implicit Types Φ Ψ : val Λ → iProp Σ.
 Implicit Types v : val Λ.
@@ -75,17 +76,29 @@ Proof.
   iIntros (v) "Hv". by iApply "HΦ".
 Qed.
 
-Lemma ht_atomic p E1 E2 P P' Φ Φ' e :
-  StronglyAtomic e →
+Lemma ht_atomic' p E1 E2 P P' Φ Φ' e :
+  StronglyAtomic e ∨ p ∧ Atomic e →
   (P ={E1,E2}=> P') ∧ {{ P' }} e @ p; E2 {{ Φ' }} ∧ (∀ v, Φ' v ={E2,E1}=> Φ v)
   ⊢ {{ P }} e @ p; E1 {{ Φ }}.
 Proof.
-  iIntros (?) "(#Hvs & #Hwp & #HΦ) !# HP". iApply (wp_atomic _ _ E2); auto.
+  iIntros (?) "(#Hvs & #Hwp & #HΦ) !# HP". iApply (wp_atomic' _ _ E2); auto.
   iMod ("Hvs" with "HP") as "HP". iModIntro.
   iApply (wp_wand with "[HP]"); [by iApply "Hwp"|].
   iIntros (v) "Hv". by iApply "HΦ".
 Qed.
 
+Lemma ht_strong_atomic p E1 E2 P P' Φ Φ' e :
+  StronglyAtomic e →
+  (P ={E1,E2}=> P') ∧ {{ P' }} e @ p; E2 {{ Φ' }} ∧ (∀ v, Φ' v ={E2,E1}=> Φ v)
+  ⊢ {{ P }} e @ p; E1 {{ Φ }}.
+Proof. by eauto using ht_atomic'. Qed.
+
+Lemma ht_atomic E1 E2 P P' Φ Φ' e :
+  Atomic e →
+  (P ={E1,E2}=> P') ∧ {{ P' }} e @ E2 {{ Φ' }} ∧ (∀ v, Φ' v ={E2,E1}=> Φ v)
+  ⊢ {{ P }} e @ E1 {{ Φ }}.
+Proof. by eauto using ht_atomic'. Qed.
+
 Lemma ht_bind `{LanguageCtx Λ K} p E P Φ Φ' e :
   {{ P }} e @ p; E {{ Φ }} ∧ (∀ v, {{ Φ v }} K (of_val v) @ p; E {{ Φ' }})
   ⊢ {{ P }} K e @ p; E {{ Φ' }}.
diff --git a/theories/program_logic/weakestpre.v b/theories/program_logic/weakestpre.v
index b205ee3995218edc155578a5ccccbea508f96246..12c77165ce3222d1942dd8cf2247838deed7ff38 100644
--- a/theories/program_logic/weakestpre.v
+++ b/theories/program_logic/weakestpre.v
@@ -165,6 +165,7 @@ Notation "'{{{' P } } } e ? {{{ 'RET' pat ; Q } } }" :=
 
 Section wp.
 Context `{irisG Λ Σ}.
+Implicit Types p : bool.
 Implicit Types P : iProp Σ.
 Implicit Types Φ : val Λ → iProp Σ.
 Implicit Types v : val Λ.
@@ -231,8 +232,8 @@ Qed.
 Lemma wp_fupd p E e Φ : WP e @ p; E {{ v, |={E}=> Φ v }} ⊢ WP e @ p; E {{ Φ }}.
 Proof. iIntros "H". iApply (wp_strong_mono p E); try iFrame; auto. Qed.
 
-Lemma wp_atomic p E1 E2 e Φ :
-  StronglyAtomic e →
+Lemma wp_atomic' p E1 E2 e Φ :
+  StronglyAtomic e ∨ p ∧ Atomic e →
   (|={E1,E2}=> WP e @ p; E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ p; E1 {{ Φ }}.
 Proof.
   iIntros (Hatomic) "H". rewrite !wp_unfold /wp_pre.
@@ -240,9 +241,15 @@ Proof.
   { by iDestruct "H" as ">>> $". }
   iIntros (σ1) "Hσ". iMod "H". iMod ("H" $! σ1 with "Hσ") as "[$ H]".
   iModIntro. iNext. iIntros (e2 σ2 efs Hstep).
-  destruct (Hatomic _ _ _ _ Hstep) as [v <-%of_to_val].
-  iMod ("H" with "[#]") as "($ & H & $)"; first done.
-  iMod (wp_value_inv with "H") as ">H". by iApply wp_value'.
+  destruct Hatomic as [Hstrong|[? Hweak]].
+  - destruct (Hstrong _ _ _ _ Hstep) as [v <-%of_to_val].
+    iMod ("H" with "[#]") as "($ & H & $)"; first done.
+    iMod (wp_value_inv with "H") as ">H". by iApply wp_value'.
+  - destruct p; last done. iMod ("H" with "[//]") as "(Hphy & H & $)".
+    rewrite !wp_unfold /wp_pre. destruct (to_val e2).
+    + iDestruct "H" as ">> $". by iFrame.
+    + iMod ("H" with "[$]") as "[H _]".
+      iDestruct "H" as %(? & ? & ? & ?). by edestruct (Hweak _ _ _ _ Hstep).
 Qed.
 
 Lemma wp_step_fupd p E1 E2 e P Φ :
@@ -307,6 +314,15 @@ Lemma wp_value_fupd p E Φ e v `{!IntoVal e v} :
   (|={E}=> Φ v) ⊢ WP e @ p; E {{ Φ }}.
 Proof. intros. rewrite -wp_fupd -wp_value //. Qed.
 
+Lemma wp_strong_atomic p E1 E2 e Φ :
+  StronglyAtomic e →
+  (|={E1,E2}=> WP e @ p; E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ p; E1 {{ Φ }}.
+Proof. by eauto using wp_atomic'. Qed.
+Lemma wp_atomic E1 E2 e Φ :
+  Atomic e →
+  (|={E1,E2}=> WP e @ E2 {{ v, |={E2,E1}=> Φ v }}) ⊢ WP e @ E1 {{ Φ }}.
+Proof. by eauto using wp_atomic'. Qed.
+
 Lemma wp_frame_l p E e Φ R : R ∗ WP e @ p; E {{ Φ }} ⊢ WP e @ p; E {{ v, R ∗ Φ v }}.
 Proof. iIntros "[??]". iApply (wp_strong_mono p E E _ Φ); try iFrame; eauto. Qed.
 Lemma wp_frame_r p E e Φ R : WP e @ p; E {{ Φ }} ∗ R ⊢ WP e @ p; E {{ v, Φ v ∗ R }}.
@@ -369,9 +385,16 @@ Section proofmode_classes.
   Proof. by rewrite /ElimModal fupd_frame_r wand_elim_r fupd_wp. Qed.
 
   (* lower precedence, if possible, it should persistently pick elim_upd_fupd_wp *)
-  Global Instance elim_modal_fupd_wp_atomic E1 E2 e P Φ :
+  Global Instance elim_modal_fupd_wp_strong_atomic E1 E2 e P Φ :
     StronglyAtomic e →
     ElimModal (|={E1,E2}=> P) P
             (WP e @ p; E1 {{ Φ }}) (WP e @ p; E2 {{ v, |={E2,E1}=> Φ v }})%I | 100.
+  Proof. intros. by rewrite /ElimModal fupd_frame_r wand_elim_r wp_strong_atomic. Qed.
+
+  (* lower precedence than elim_modal_fupd_wp_strong_atomic (for no good reason) *)
+  Global Instance elim_modal_fupd_wp_atomic E1 E2 e P Φ :
+    Atomic e →
+    ElimModal (|={E1,E2}=> P) P
+            (WP e @ E1 {{ Φ }}) (WP e @ E2 {{ v, |={E2,E1}=> Φ v }})%I | 110.
   Proof. intros. by rewrite /ElimModal fupd_frame_r wand_elim_r wp_atomic. Qed.
 End proofmode_classes.
diff --git a/theories/tests/ipm_paper.v b/theories/tests/ipm_paper.v
index 0922cd5bbb09d343c208b52172a4c0fb378479f5..6834c5c5e3928fd626f706c6eda0a8daf90d433e 100644
--- a/theories/tests/ipm_paper.v
+++ b/theories/tests/ipm_paper.v
@@ -101,7 +101,7 @@ update modalities (which we did not cover in the paper). Normally we use these
 mask changing update modalities directly in our proofs, but in this file we use
 the first prove the rule as a lemma, and then use that. *)
 Lemma wp_inv_open `{irisG Λ Σ} N E P e Φ :
-  nclose N ⊆ E → StronglyAtomic e →
+  nclose N ⊆ E → Atomic e →
   inv N P ∗ (▷ P -∗ WP e @ E ∖ ↑N {{ v, ▷ P ∗ Φ v }}) ⊢ WP e @ E {{ Φ }}.
 Proof.
   iIntros (??) "[#Hinv Hwp]".