diff --git a/Pantograph/Goal.lean b/Pantograph/Goal.lean
index 044e9e7..ba066f3 100644
--- a/Pantograph/Goal.lean
+++ b/Pantograph/Goal.lean
@@ -521,9 +521,8 @@ protected def GoalState.tryTactic (state: GoalState) (site : Site) (tactic: Stri
   let .some goal := state.actingGoal? site | throwNoGoals
   if let .some fragment := state.fragments[goal]? then
     return ← withCapturingError do
-      let (moreFragments, state') ← state.step' site (fragment.step goal tactic)
-      let fragments := moreFragments.fold (init := state.fragments.erase goal) λ acc mvarId f =>
-        acc.insert mvarId f
+      let (fragments, state') ← state.step' site do
+        fragment.step goal tactic $ state.fragments.erase goal
       return { state' with fragments }
   -- Normal tactic without fragment
   let tactic ← match Parser.runParserCategory
diff --git a/Pantograph/Tactic/Fragment.lean b/Pantograph/Tactic/Fragment.lean
index 9677042..2138801 100644
--- a/Pantograph/Tactic/Fragment.lean
+++ b/Pantograph/Tactic/Fragment.lean
@@ -72,7 +72,7 @@ protected def Fragment.exit (fragment : Fragment) (goal : MVarId) (fragments : F
   | .convSentinel _ =>
     return fragments.erase goal
 
-protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String)
+protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String) (map : FragmentMap)
   : Elab.Tactic.TacticM FragmentMap := goal.withContext do
   assert! ¬ (← goal.isAssigned)
   match fragment with
@@ -127,11 +127,11 @@ protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String)
     let goals := [ mvarBranch ] ++ remainder?.toList
     Elab.Tactic.setGoals goals
     match remainder? with
-    | .some goal => return FragmentMap.empty.insert goal $ .calc (.some rhs)
-    | .none => return .empty
+    | .some goal => return map.erase goal |>.insert goal $ .calc (.some rhs)
+    | .none => return map
   | .conv .. => do
     throwError "Direct operation on conversion tactic parent goal is not allowed"
-  | fragment@(.convSentinel _) => do
+  | fragment@(.convSentinel parent) => do
     assert! isLHSGoal? (← goal.getType) |>.isSome
     let tactic ← match Parser.runParserCategory
       (env := ← MonadEnv.getEnv)
@@ -143,8 +143,14 @@ protected def Fragment.step (fragment : Fragment) (goal : MVarId) (s : String)
     let oldGoals ← Elab.Tactic.getGoals
     -- Label newly generated goals as conv sentinels
     Elab.Tactic.evalTactic tactic
-    let newGoals := (← Elab.Tactic.getUnsolvedGoals).filter λ g => ¬ (oldGoals.contains g)
-    return newGoals.foldl (init := FragmentMap.empty) λ acc g =>
+    let newGoals ← (← Elab.Tactic.getUnsolvedGoals).filterM λ g => do
+      -- conv tactic might generate non-conv goals
+      if oldGoals.contains g then
+        return false
+      let target ← g.getType
+      return isLHSGoal? (← g.getType) |>.isSome
+    -- FIXME: Conclude the conv by exiting the parent fragment if new goals is empty
+    return newGoals.foldl (init := map) λ acc g =>
       acc.insert g fragment
 
 end Pantograph
diff --git a/Test/Common.lean b/Test/Common.lean
index 34ce07b..bbc8725 100644
--- a/Test/Common.lean
+++ b/Test/Common.lean
@@ -71,6 +71,8 @@ def GoalState.get! (state: GoalState) (i: Nat): MVarId := state.goals[i]!
 def GoalState.tacticOn (state: GoalState) (goalId: Nat) (tactic: String) := state.tryTactic (state.get! goalId) tactic
 def GoalState.tacticOn' (state: GoalState) (goalId: Nat) (tactic: TSyntax `tactic) :=
   state.tryTacticM (state.get! goalId) (Elab.Tactic.evalTactic tactic) true
+def GoalState.tryTacticOnMain (state : GoalState) (tactic : String) :=
+  state.tryTactic (.prefer state.goals[0]!) tactic
 
 def TacticResult.toString : TacticResult → String
   | .success state _messages => s!".success ({state.goals.length} goals)"
diff --git a/Test/Tactic/Fragment.lean b/Test/Tactic/Fragment.lean
index d32da91..e4431c7 100644
--- a/Test/Tactic/Fragment.lean
+++ b/Test/Tactic/Fragment.lean
@@ -5,10 +5,9 @@ open Lean
 
 namespace Pantograph.Test.Tactic.Fragment
 
-private def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none):
+private def buildGoal (nameType: List (String × String)) (target: String):
     Protocol.Goal :=
   {
-    userName?,
     target := { pp? := .some target},
     vars := (nameType.map fun x => ({
       userName := x.fst,
@@ -133,6 +132,55 @@ def test_conv: TestM Unit := do
       let free := [("a", "Nat"), ("b", "Nat"), ("c1", "Nat"), ("c2", "Nat"), ("h", h)] ++ free
       buildGoal free target
 
+example (p : Prop) (x y z : Nat) : p → (p → x = y) → x + z = y + z ∧ p := by
+  intro hp hi
+  apply And.intro
+  conv =>
+    rhs
+    arg 1
+    rw [←hi]
+    rfl
+    tactic => exact hp
+  exact hp
+
+def test_conv_unshielded : TestM Unit := do
+  let rootTarget ← parseSentence "∀ (p : Prop) (x y z : Nat), p → (p → x = y) → x + z = y + z ∧ p"
+  let state ← GoalState.create rootTarget
+  let tactic := "intro p x y z hp hi"
+  let .success state _ ← state.tacticOn 0 tactic | fail "intro failed"
+  let tactic := "apply And.intro"
+  let .success state _ ← state.tacticOn 0 tactic | fail "apply failed"
+  let .success state _ ← state.convEnter (.prefer state.goals[0]!) | fail "Cannot enter conversion tactic mode"
+  let .success state _ ← state.tryTacticOnMain "rhs" | fail "rhs failed"
+  let tactic := "arg 1"
+  let .success state _ ← state.tryTacticOnMain tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      { interiorGoal [] "y" with isConversion := true },
+      { interiorGoal [] "p" with userName? := "right", },
+    ]
+  let tactic := "rw [←hi]"
+  let .success state _ ← state.tryTacticOnMain tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" state.goals.length 3
+  let tactic := "rfl"
+  let .success state _ ← state.tryTacticOnMain tactic | fail s!"{tactic} failed"
+  checkEq s!"  {tactic}" ((← state.serializeGoals).map (·.devolatilize))
+    #[
+      interiorGoal [] "p",
+      { interiorGoal [] "p" with userName? := "right", },
+    ]
+  checkEq "  (n goals)" state.goals.length 2
+  let tactic := "exact hp"
+  let .success state _ ← state.tryTacticOnMain tactic | fail s!"{tactic} failed"
+  let tactic := "exact hp"
+  let .success state _ ← state.tryTacticOnMain tactic | fail s!"{tactic} failed"
+  let root? := state.rootExpr?
+  checkTrue "root" root?.isSome
+  where
+  interiorGoal (free: List (String × String)) (target: String) :=
+    let free := [("p", "Prop"), ("x", "Nat"), ("y", "Nat"), ("z", "Nat"), ("hp", "p"), ("hi", "p → x = y")] ++ free
+    buildGoal free target
+
 example : ∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d := by
   intro a b c d h1 h2
   calc a + b = b + c := by apply h1
@@ -158,7 +206,7 @@ def test_calc: TestM Unit := do
       return ()
   addTest $ LSpec.check s!"calc {pred} := _" ((← state2.serializeGoals).map (·.devolatilize) =
     #[
-      interiorGoal [] "a + b = b + c" (.some "calc"),
+      { interiorGoal [] "a + b = b + c" with userName? := .some "calc" },
       interiorGoal [] "b + c = c + d"
     ])
   addTest $ LSpec.test "(2.0 prev rhs)" (state2.calcPrevRhsOf? (state2.get! 0) |>.isNone)
@@ -183,7 +231,7 @@ def test_calc: TestM Unit := do
       return ()
   addTest $ LSpec.check s!"calc {pred} := _" ((← state4.serializeGoals).map (·.devolatilize) =
     #[
-      interiorGoal [] "b + c = c + d" (.some "calc")
+      { interiorGoal [] "b + c = c + d" with userName? := .some "calc" },
     ])
   addTest $ LSpec.test "(4.0 prev rhs)" (state4.calcPrevRhsOf? (state4.get! 0) |>.isNone)
   let tactic := "apply h2"
@@ -194,14 +242,15 @@ def test_calc: TestM Unit := do
       return ()
   addTest $ LSpec.test "(4m root)" state4m.rootExpr?.isSome
   where
-    interiorGoal (free: List (String × String)) (target: String) (userName?: Option String := .none) :=
+    interiorGoal (free: List (String × String)) (target: String) :=
       let free := [("a", "Nat"), ("b", "Nat"), ("c", "Nat"), ("d", "Nat"),
         ("h1", "a + b = b + c"), ("h2", "b + c = c + d")] ++ free
-      buildGoal free target userName?
+      buildGoal free target
 
 def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
   [
     ("conv", test_conv),
+    ("conv unshielded", test_conv_unshielded),
     ("calc", test_calc),
   ] |>.map (λ (name, t) => (name, runTestTermElabM env t))