diff --git a/src/Lean/Elab/Tactic/Simp.lean b/src/Lean/Elab/Tactic/Simp.lean
index 1616aa69e1c0..8373be635d2b 100644
--- a/src/Lean/Elab/Tactic/Simp.lean
+++ b/src/Lean/Elab/Tactic/Simp.lean
@@ -342,7 +342,8 @@ def mkSimpContext (stx : Syntax) (eraseLocal : Bool) (kind := SimpKind.simp)
   let dischargeWrapper ← mkDischargeWrapper stx[2]
   let simpOnly := !stx[simpOnlyPos].isNone
   let simpTheorems ← if simpOnly then
-    simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
+    -- `eq_self` and `iff_self` are given a priority just above default, since they prove the goal
+    simpOnlyBuiltins.foldlM (·.addConst · (prio := eval_prio default+10)) ({} : SimpTheorems)
   else
     simpTheorems
   let simprocs ← if simpOnly then pure {} else Simp.getSimprocs
diff --git a/src/Lean/Meta/Tactic/Simp/Rewrite.lean b/src/Lean/Meta/Tactic/Simp/Rewrite.lean
index 595222601741..f630f6d1ab3e 100644
--- a/src/Lean/Meta/Tactic/Simp/Rewrite.lean
+++ b/src/Lean/Meta/Tactic/Simp/Rewrite.lean
@@ -216,7 +216,8 @@ where
       trace[Debug.Meta.Tactic.simp] "no theorems found for {tag}-rewriting {e}"
       return none
     else
-      let candidates := candidates.insertionSort fun e₁ e₂ => e₁.1.priority > e₂.1.priority
+      -- `candidates` is reversed so that more specific matches are tried first
+      let candidates := candidates.reverse.insertionSort fun e₁ e₂ => e₁.1.priority > e₂.1.priority
       for (thm, numExtraArgs) in candidates do
         unless inErasedSet thm || (rflOnly && !thm.rfl) do
           if let some result ← tryTheoremWithExtraArgs? e thm numExtraArgs then