diff --git a/clang-tools-extra/pseudo/include/clang-pseudo/GLR.h b/clang-tools-extra/pseudo/include/clang-pseudo/GLR.h
--- a/clang-tools-extra/pseudo/include/clang-pseudo/GLR.h
+++ b/clang-tools-extra/pseudo/include/clang-pseudo/GLR.h
@@ -132,34 +132,17 @@
 const ForestNode &glrParse(const TokenStream &Code, const ParseParams &Params,
                            SymbolID StartSymbol);
 
-// An active stack head can have multiple available actions (reduce/reduce
-// actions, reduce/shift actions).
-// A step is any one action applied to any one stack head.
-struct ParseStep {
-  // A specific stack head.
-  const GSS::Node *Head = nullptr;
-  // An action associated with the head.
-  LRTable::Action Action = LRTable::Action::sentinel();
-};
-// A callback is invoked whenever a new GSS head is created during the GLR
-// parsing process (glrShift, or glrReduce).
-using NewHeadCallback = std::function<void(const GSS::Node *)>;
-// Apply all PendingShift actions on a given GSS state, newly-created heads are
-// passed to the callback.
-//
-// When this function returns, PendingShift is empty.
+// Shift a token onto all OldHeads, placing the results into NewHeads.
 //
 // Exposed for testing only.
-void glrShift(std::vector<ParseStep> &PendingShift, const ForestNode &NextTok,
-              const ParseParams &Params, NewHeadCallback NewHeadCB);
-// Applies PendingReduce actions, until no more reduce actions are available.
-//
-// When this function returns, PendingReduce is empty. Calls to NewHeadCB may
-// add elements to PendingReduce
+void glrShift(llvm::ArrayRef<const GSS::Node *> OldHeads,
+              const ForestNode &NextTok, const ParseParams &Params,
+              std::vector<const GSS::Node *> &NewHeads);
+// Applies available reductions on Heads, appending resulting heads to the list.
 //
 // Exposed for testing only.
-void glrReduce(std::vector<ParseStep> &PendingReduce, const ParseParams &Params,
-               NewHeadCallback NewHeadCB);
+void glrReduce(std::vector<const GSS::Node *> &Heads, SymbolID Lookahead,
+               const ParseParams &Params);
 
 } // namespace pseudo
 } // namespace clang
diff --git a/clang-tools-extra/pseudo/include/clang-pseudo/grammar/LRTable.h b/clang-tools-extra/pseudo/include/clang-pseudo/grammar/LRTable.h
--- a/clang-tools-extra/pseudo/include/clang-pseudo/grammar/LRTable.h
+++ b/clang-tools-extra/pseudo/include/clang-pseudo/grammar/LRTable.h
@@ -128,7 +128,12 @@
   llvm::ArrayRef<Action> getActions(StateID State, SymbolID Terminal) const;
   // Returns the state after we reduce a nonterminal.
   // Expected to be called by LR parsers.
+  // REQUIRES: Nonterminal is valid here.
   StateID getGoToState(StateID State, SymbolID Nonterminal) const;
+  // Returns the state after we shift a terminal.
+  // Expected to be called by LR parsers.
+  // If the terminal is invalid here, returns None.
+  llvm::Optional<StateID> getShiftState(StateID State, SymbolID Terminal) const;
 
   // Looks up available actions.
   // Returns empty if no available actions in the table.
diff --git a/clang-tools-extra/pseudo/lib/GLR.cpp b/clang-tools-extra/pseudo/lib/GLR.cpp
--- a/clang-tools-extra/pseudo/lib/GLR.cpp
+++ b/clang-tools-extra/pseudo/lib/GLR.cpp
@@ -45,68 +45,39 @@
   (void)G;
   auto &GSS = Params.GSStack;
 
-  // Lists of active shift, reduce actions.
-  std::vector<ParseStep> PendingShift, PendingReduce;
-  auto AddSteps = [&](const GSS::Node *Head, SymbolID NextTok) {
-    for (const auto &Action : Params.Table.getActions(Head->State, NextTok)) {
-      switch (Action.kind()) {
-      case LRTable::Action::Shift:
-        PendingShift.push_back({Head, Action});
-        break;
-      case LRTable::Action::Reduce:
-        PendingReduce.push_back({Head, Action});
-        break;
-      default:
-        llvm_unreachable("unexpected action kind!");
-      }
-    }
-  };
   StateID StartState = Params.Table.getStartState(StartSymbol);
-  std::vector<const GSS::Node *> NewHeads = {
-      GSS.addNode(/*State=*/StartState,
-                  /*ForestNode=*/nullptr, {})};
+  std::vector<const GSS::Node *> Heads = {GSS.addNode(/*State=*/StartState,
+                                                      /*ForestNode=*/nullptr,
+                                                      {})};
+  std::vector<const GSS::Node *> NextHeads;
   auto MaybeGC = [&, Roots(std::vector<const GSS::Node *>{}), I(0u)]() mutable {
-    assert(PendingShift.empty() && PendingReduce.empty() &&
-           "Running GC at the wrong time!");
-
+    assert(NextHeads.empty() && "Running GC at the wrong time!");
     if (++I != 20) // Run periodically to balance CPU and memory usage.
       return;
     I = 0;
 
     // We need to copy the list: Roots is consumed by the GC.
-    Roots = NewHeads;
+    Roots = Heads;
     GSS.gc(std::move(Roots));
   };
-  for (const ForestNode &Terminal : Terminals) {
-    LLVM_DEBUG(llvm::dbgs() << llvm::formatv("Next token {0} (id={1})\n",
-                                             G.symbolName(Terminal.symbol()),
-                                             Terminal.symbol()));
-    for (const auto *Head : NewHeads)
-      AddSteps(Head, Terminal.symbol());
-    NewHeads.clear();
-    glrReduce(PendingReduce, Params,
-              [&](const GSS::Node * NewHead) {
-                // A reduce will enable more steps.
-                AddSteps(NewHead, Terminal.symbol());
-              });
-
-    glrShift(PendingShift, Terminal, Params,
-             [&](const GSS::Node *NewHead) { NewHeads.push_back(NewHead); });
+  for (unsigned I = 0; I < Terminals.size(); ++I) {
+    LLVM_DEBUG(llvm::dbgs() << llvm::formatv(
+                   "Next token {0} (id={1})\n",
+                   G.symbolName(Terminals[I].symbol()), Terminals[I].symbol()));
+
+    glrShift(Heads, Terminals[I], Params, NextHeads);
+
+    SymbolID Lookahead = I + 1 == Terminals.size() ? tokenSymbol(tok::eof)
+                                                   : Terminals[I + 1].symbol();
+    glrReduce(NextHeads, Lookahead, Params);
+
+    std::swap(Heads, NextHeads);
+    NextHeads.clear();
     MaybeGC();
   }
-  LLVM_DEBUG(llvm::dbgs() << llvm::formatv("Next is eof\n"));
-  for (const auto *Heads : NewHeads)
-    AddSteps(Heads, tokenSymbol(tok::eof));
+  LLVM_DEBUG(llvm::dbgs() << llvm::formatv("Reached eof\n"));
 
   StateID AcceptState = Params.Table.getGoToState(StartState, StartSymbol);
-  // Collect new heads created from the final reduce.
-  std::vector<const GSS::Node*> Heads;
-  glrReduce(PendingReduce, Params, [&](const GSS::Node *NewHead) {
-    Heads.push_back(NewHead);
-    // A reduce will enable more steps.
-    AddSteps(NewHead, tokenSymbol(tok::eof));
-  });
-
   const ForestNode *Result = nullptr;
   for (const auto *Head : Heads) {
     if (Head->State == AcceptState) {
@@ -138,42 +109,40 @@
 // After the shift action, the GSS is:
 //   0---1---2---4
 //       └---3---┘
-void glrShift(std::vector<ParseStep> &PendingShift, const ForestNode &NewTok,
-              const ParseParams &Params, NewHeadCallback NewHeadCB) {
+void glrShift(llvm::ArrayRef<const GSS::Node *> OldHeads,
+              const ForestNode &NewTok, const ParseParams &Params,
+              std::vector<const GSS::Node *> &NewHeads) {
   assert(NewTok.kind() == ForestNode::Terminal);
-  assert(llvm::all_of(PendingShift,
-                      [](const ParseStep &Step) {
-                        return Step.Action.kind() == LRTable::Action::Shift;
-                      }) &&
-         "Pending shift actions must be shift actions");
   LLVM_DEBUG(llvm::dbgs() << llvm::formatv("  Shift {0} ({1} active heads):\n",
                                            Params.G.symbolName(NewTok.symbol()),
-                                           PendingShift.size()));
+                                           OldHeads.size()));
 
   // We group pending shifts by their target state so we can merge them.
-  llvm::stable_sort(PendingShift, [](const ParseStep &L, const ParseStep &R) {
-    return L.Action.getShiftState() < R.Action.getShiftState();
-  });
-  auto Rest = llvm::makeArrayRef(PendingShift);
+  llvm::SmallVector<std::pair<StateID, const GSS::Node *>, 8> Shifts;
+  for (const auto *H : OldHeads)
+    if (auto S = Params.Table.getShiftState(H->State, NewTok.symbol()))
+      Shifts.push_back({*S, H});
+  llvm::stable_sort(Shifts, llvm::less_first{});
+
+  auto Rest = llvm::makeArrayRef(Shifts);
   llvm::SmallVector<const GSS::Node *> Parents;
   while (!Rest.empty()) {
     // Collect the batch of PendingShift that have compatible shift states.
     // Their heads become TempParents, the parents of the new GSS node.
-    StateID NextState = Rest.front().Action.getShiftState();
+    StateID NextState = Rest.front().first;
 
     Parents.clear();
     for (const auto &Base : Rest) {
-      if (Base.Action.getShiftState() != NextState)
+      if (Base.first != NextState)
         break;
-      Parents.push_back(Base.Head);
+      Parents.push_back(Base.second);
     }
     Rest = Rest.drop_front(Parents.size());
 
     LLVM_DEBUG(llvm::dbgs() << llvm::formatv("    --> S{0} ({1} heads)\n",
                                              NextState, Parents.size()));
-    NewHeadCB(Params.GSStack.addNode(NextState, &NewTok, Parents));
+    NewHeads.push_back(Params.GSStack.addNode(NextState, &NewTok, Parents));
   }
-  PendingShift.clear();
 }
 
 namespace {
@@ -231,8 +200,9 @@
 //   After reducing 3 by `pointer := class-name STAR` and
 //                  2 by`enum-name := class-name STAR`:
 //     0--5(pointer)       // 5 is goto(0, pointer)
-void glrReduce(std::vector<ParseStep> &PendingReduce, const ParseParams &Params,
-               NewHeadCallback NewHeadCB) {
+void glrReduce(std::vector<const GSS::Node *> &Heads, SymbolID Lookahead,
+               const ParseParams &Params) {
+  assert(isToken(Lookahead));
   // There are two interacting complications:
   // 1.  Performing one reduce can unlock new reduces on the newly-created head.
   // 2a. The ambiguous ForestNodes must be complete (have all sequence nodes).
@@ -291,6 +261,10 @@
   KeyedQueue<Family, PushSpec> Sequences;
 
   Sequence TempSequence;
+
+  // We treat Heads as a queue of Pop operations still to be performed.
+  // NextPopHead is our position within it.
+  unsigned NextPopHead = 0;
   // Pop walks up the parent chain(s) for a reduction from Head by to Rule.
   // Once we reach the end, record the bases and sequences.
   auto Pop = [&](const GSS::Node *Head, RuleID RID) {
@@ -312,9 +286,16 @@
     DFS(Head, 0, DFS);
   };
   auto PopPending = [&] {
-    for (const ParseStep &Pending : PendingReduce)
-      Pop(Pending.Head, Pending.Action.getReduceRule());
-    PendingReduce.clear();
+    for (; NextPopHead < Heads.size(); ++NextPopHead) {
+      // FIXME: if there's exactly one head in the queue, and the pop stage
+      // is trivial, we could pop + push without touching the expensive queues.
+      for (const auto &A :
+           Params.Table.getActions(Heads[NextPopHead]->State, Lookahead)) {
+        if (A.kind() != LRTable::Action::Reduce)
+          continue;
+        Pop(Heads[NextPopHead], A.getReduceRule());
+      }
+    }
   };
 
   std::vector<std::pair</*Goto*/ StateID, const GSS::Node *>> FamilyBases;
@@ -378,10 +359,7 @@
         Parents.push_back(Base.second);
       }
       BasesLeft = BasesLeft.drop_front(Parents.size());
-
-      // Invoking the callback for new heads, a real GLR parser may add new
-      // reduces to the PendingReduce queue!
-      NewHeadCB(Params.GSStack.addNode(NextState, Parsed, Parents));
+      Heads.push_back(Params.GSStack.addNode(NextState, Parsed, Parents));
     }
     PopPending();
   }
diff --git a/clang-tools-extra/pseudo/lib/grammar/LRTable.cpp b/clang-tools-extra/pseudo/lib/grammar/LRTable.cpp
--- a/clang-tools-extra/pseudo/lib/grammar/LRTable.cpp
+++ b/clang-tools-extra/pseudo/lib/grammar/LRTable.cpp
@@ -72,6 +72,17 @@
   return OS.str();
 }
 
+llvm::Optional<LRTable::StateID>
+LRTable::getShiftState(StateID State, SymbolID Terminal) const {
+  // FIXME: we spend a significant amount of time on misses here.
+  // We could consider storing a std::bitset for a cheaper test?
+  assert(pseudo::isToken(Terminal) && "expected terminal symbol!");
+  for (const auto &Result : getActions(State, Terminal))
+    if (Result.kind() == Action::Shift)
+      return Result.getShiftState(); // unique: no shift/shift conflicts.
+  return llvm::None;
+}
+
 llvm::ArrayRef<LRTable::Action> LRTable::getActions(StateID State,
                                                     SymbolID Terminal) const {
   assert(pseudo::isToken(Terminal) && "expect terminal symbol!");
diff --git a/clang-tools-extra/pseudo/unittests/GLRTest.cpp b/clang-tools-extra/pseudo/unittests/GLRTest.cpp
--- a/clang-tools-extra/pseudo/unittests/GLRTest.cpp
+++ b/clang-tools-extra/pseudo/unittests/GLRTest.cpp
@@ -7,8 +7,8 @@
 //===----------------------------------------------------------------------===//
 
 #include "clang-pseudo/GLR.h"
-#include "clang-pseudo/grammar/Grammar.h"
 #include "clang-pseudo/Token.h"
+#include "clang-pseudo/grammar/Grammar.h"
 #include "clang/Basic/LangOptions.h"
 #include "clang/Basic/TokenKinds.h"
 #include "llvm/ADT/StringExtras.h"
@@ -31,6 +31,7 @@
 
 using Action = LRTable::Action;
 using testing::AllOf;
+using testing::UnorderedElementsAre;
 
 MATCHER_P(state, StateID, "") { return arg->State == StateID; }
 MATCHER_P(parsedSymbol, FNode, "") { return arg->Payload == FNode; }
@@ -83,17 +84,10 @@
     return 0;
   }
 
-  NewHeadCallback captureNewHeads() {
-    return [this](const GSS::Node *NewHead) {
-      NewHeadResults.push_back(NewHead);
-    };
-  };
-
 protected:
   std::unique_ptr<Grammar> G;
   ForestArena Arena;
   GSS GSStack;
-  std::vector<const GSS::Node*> NewHeadResults;
 };
 
 TEST_F(GLRTest, ShiftMergingHeads) {
@@ -109,31 +103,32 @@
   //   └---3---5
   auto *GSSNode0 =
       GSStack.addNode(/*State=*/0, /*ForestNode=*/nullptr, /*Parents=*/{});
-  auto *GSSNode1 = GSStack.addNode(/*State=*/0, /*ForestNode=*/nullptr,
+  auto *GSSNode1 = GSStack.addNode(/*State=*/1, /*ForestNode=*/nullptr,
                                    /*Parents=*/{GSSNode0});
-  auto *GSSNode2 = GSStack.addNode(/*State=*/0, /*ForestNode=*/nullptr,
+  auto *GSSNode2 = GSStack.addNode(/*State=*/2, /*ForestNode=*/nullptr,
                                    /*Parents=*/{GSSNode0});
-  auto *GSSNode3 = GSStack.addNode(/*State=*/0, /*ForestNode=*/nullptr,
+  auto *GSSNode3 = GSStack.addNode(/*State=*/3, /*ForestNode=*/nullptr,
                                    /*Parents=*/{GSSNode0});
 
   buildGrammar({}, {}); // Create a fake empty grammar.
-  LRTable T = LRTable::buildForTests(G->table(), /*Entries=*/{});
+  LRTable T =
+      LRTable::buildForTests(G->table(), /*Entries=*/{
+                                 {1, tokenSymbol(tok::semi), Action::shift(4)},
+                                 {2, tokenSymbol(tok::semi), Action::shift(4)},
+                                 {3, tokenSymbol(tok::semi), Action::shift(5)},
+                             });
 
   ForestNode &SemiTerminal = Arena.createTerminal(tok::semi, 0);
-  std::vector<ParseStep> PendingShift = {
-      {GSSNode1, Action::shift(4)},
-      {GSSNode3, Action::shift(5)},
-      {GSSNode2, Action::shift(4)},
-  };
-  glrShift(PendingShift, SemiTerminal, {*G, T, Arena, GSStack},
-           captureNewHeads());
-
-  EXPECT_THAT(NewHeadResults, testing::UnorderedElementsAre(
-                                  AllOf(state(4), parsedSymbol(&SemiTerminal),
-                                        parents({GSSNode1, GSSNode2})),
-                                  AllOf(state(5), parsedSymbol(&SemiTerminal),
-                                        parents({GSSNode3}))))
-      << NewHeadResults;
+  std::vector<const GSS::Node *> NewHeads;
+  glrShift({GSSNode1, GSSNode2, GSSNode3}, SemiTerminal,
+           {*G, T, Arena, GSStack}, NewHeads);
+
+  EXPECT_THAT(NewHeads,
+              UnorderedElementsAre(AllOf(state(4), parsedSymbol(&SemiTerminal),
+                                         parents({GSSNode1, GSSNode2})),
+                                   AllOf(state(5), parsedSymbol(&SemiTerminal),
+                                         parents({GSSNode3}))))
+      << NewHeads;
 }
 
 TEST_F(GLRTest, ReduceConflictsSplitting) {
@@ -147,25 +142,29 @@
                {"class-name := IDENTIFIER", "enum-name := IDENTIFIER"});
 
   LRTable Table = LRTable::buildForTests(
-      G->table(), {{/*State=*/0, id("class-name"), Action::goTo(2)},
-                   {/*State=*/0, id("enum-name"), Action::goTo(3)}});
+      G->table(), {
+                      {/*State=*/0, id("class-name"), Action::goTo(2)},
+                      {/*State=*/0, id("enum-name"), Action::goTo(3)},
+                      {/*State=*/1, tokenSymbol(tok::l_brace),
+                       Action::reduce(ruleFor("class-name"))},
+                      {/*State=*/1, tokenSymbol(tok::l_brace),
+                       Action::reduce(ruleFor("enum-name"))},
+                  });
 
   const auto *GSSNode0 =
       GSStack.addNode(/*State=*/0, /*ForestNode=*/nullptr, /*Parents=*/{});
   const auto *GSSNode1 =
-      GSStack.addNode(3, &Arena.createTerminal(tok::identifier, 0), {GSSNode0});
-
-  std::vector<ParseStep> PendingReduce = {
-      {GSSNode1, Action::reduce(ruleFor("class-name"))},
-      {GSSNode1, Action::reduce(ruleFor("enum-name"))}};
-  glrReduce(PendingReduce, {*G, Table, Arena, GSStack},
-            captureNewHeads());
-  EXPECT_THAT(NewHeadResults,
-              testing::UnorderedElementsAre(
-                  AllOf(state(2), parsedSymbolID(id("class-name")),
-                        parents({GSSNode0})),
-                  AllOf(state(3), parsedSymbolID(id("enum-name")),
-                        parents({GSSNode0})))) << NewHeadResults;
+      GSStack.addNode(1, &Arena.createTerminal(tok::identifier, 0), {GSSNode0});
+
+  std::vector<const GSS::Node *> Heads = {GSSNode1};
+  glrReduce(Heads, tokenSymbol(tok::l_brace), {*G, Table, Arena, GSStack});
+  EXPECT_THAT(Heads, UnorderedElementsAre(
+                         GSSNode1,
+                         AllOf(state(2), parsedSymbolID(id("class-name")),
+                               parents({GSSNode0})),
+                         AllOf(state(3), parsedSymbolID(id("enum-name")),
+                               parents({GSSNode0}))))
+      << Heads;
 }
 
 TEST_F(GLRTest, ReduceSplittingDueToMultipleBases) {
@@ -191,22 +190,25 @@
 
   LRTable Table = LRTable::buildForTests(
       G->table(),
-      {{/*State=*/2, id("ptr-operator"), Action::goTo(/*NextState=*/5)},
-       {/*State=*/3, id("ptr-operator"), Action::goTo(/*NextState=*/6)}});
-  std::vector<ParseStep> PendingReduce = {
-      {GSSNode4, Action::reduce(ruleFor("ptr-operator"))}};
-  glrReduce(PendingReduce, {*G, Table, Arena, GSStack},
-            captureNewHeads());
-
-  EXPECT_THAT(NewHeadResults,
-              testing::UnorderedElementsAre(
-                  AllOf(state(5), parsedSymbolID(id("ptr-operator")),
-                        parents({GSSNode2})),
-                  AllOf(state(6), parsedSymbolID(id("ptr-operator")),
-                        parents({GSSNode3})))) << NewHeadResults;
+      {
+          {/*State=*/2, id("ptr-operator"), Action::goTo(/*NextState=*/5)},
+          {/*State=*/3, id("ptr-operator"), Action::goTo(/*NextState=*/6)},
+          {/*State=*/4, tokenSymbol(tok::identifier),
+           Action::reduce(ruleFor("ptr-operator"))},
+      });
+  std::vector<const GSS::Node *> Heads = {GSSNode4};
+  glrReduce(Heads, tokenSymbol(tok::identifier), {*G, Table, Arena, GSStack});
+
+  EXPECT_THAT(Heads, UnorderedElementsAre(
+                         GSSNode4,
+                         AllOf(state(5), parsedSymbolID(id("ptr-operator")),
+                               parents({GSSNode2})),
+                         AllOf(state(6), parsedSymbolID(id("ptr-operator")),
+                               parents({GSSNode3}))))
+      << Heads;
   // Verify that the payload of the two new heads is shared, only a single
   // ptr-operator node is created in the forest.
-  EXPECT_EQ(NewHeadResults[0]->Payload, NewHeadResults[1]->Payload);
+  EXPECT_EQ(Heads[1]->Payload, Heads[2]->Payload);
 }
 
 TEST_F(GLRTest, ReduceJoiningWithMultipleBases) {
@@ -238,28 +240,28 @@
       GSStack.addNode(/*State=*/4, /*ForestNode=*/EnumNameNode,
                       /*Parents=*/{GSSNode2});
 
+  // FIXME: figure out a way to get rid of the hard-coded reduce RuleID!
   LRTable Table = LRTable::buildForTests(
       G->table(),
-      {{/*State=*/1, id("type-name"), Action::goTo(/*NextState=*/5)},
-       {/*State=*/2, id("type-name"), Action::goTo(/*NextState=*/5)}});
-  // FIXME: figure out a way to get rid of the hard-coded reduce RuleID!
-  std::vector<ParseStep> PendingReduce = {
       {
-          GSSNode3, Action::reduce(/*RuleID=*/0) // type-name := class-name
-      },
-      {
-          GSSNode4, Action::reduce(/*RuleID=*/1) // type-name := enum-name
-      }};
-  glrReduce(PendingReduce, {*G, Table, Arena, GSStack},
-            captureNewHeads());
+          {/*State=*/1, id("type-name"), Action::goTo(/*NextState=*/5)},
+          {/*State=*/2, id("type-name"), Action::goTo(/*NextState=*/5)},
+          {/*State=*/3, tokenSymbol(tok::l_paren),
+           Action::reduce(/* type-name := class-name */ 0)},
+          {/*State=*/4, tokenSymbol(tok::l_paren),
+           Action::reduce(/* type-name := enum-name */ 1)},
+      });
+  std::vector<const GSS::Node *> Heads = {GSSNode3, GSSNode4};
+  glrReduce(Heads, tokenSymbol(tok::l_paren), {*G, Table, Arena, GSStack});
 
   // Verify that the stack heads are joint at state 5 after reduces.
-  EXPECT_THAT(NewHeadResults, testing::UnorderedElementsAre(AllOf(
-                                  state(5), parsedSymbolID(id("type-name")),
-                                  parents({GSSNode1, GSSNode2}))))
-      << NewHeadResults;
+  EXPECT_THAT(Heads, UnorderedElementsAre(GSSNode3, GSSNode4,
+                                          AllOf(state(5),
+                                                parsedSymbolID(id("type-name")),
+                                                parents({GSSNode1, GSSNode2}))))
+      << Heads;
   // Verify that we create an ambiguous ForestNode of two parses of `type-name`.
-  EXPECT_EQ(NewHeadResults.front()->Payload->dumpRecursive(*G),
+  EXPECT_EQ(Heads.back()->Payload->dumpRecursive(*G),
             "[  1, end) type-name := <ambiguous>\n"
             "[  1, end) ├─type-name := class-name\n"
             "[  1, end) │ └─class-name := <opaque>\n"
@@ -296,24 +298,24 @@
       GSStack.addNode(/*State=*/4, /*ForestNode=*/StartTerminal,
                       /*Parents=*/{GSSNode2});
 
-  LRTable Table = LRTable::buildForTests(
-      G->table(), {{/*State=*/0, id("pointer"), Action::goTo(5)}});
   // FIXME: figure out a way to get rid of the hard-coded reduce RuleID!
-  std::vector<ParseStep> PendingReduce = {
-      {
-          GSSNode3, Action::reduce(/*RuleID=*/0) // pointer := class-name *
-      },
-      {
-          GSSNode4, Action::reduce(/*RuleID=*/1) // pointer := enum-name *
-      }};
-  glrReduce(PendingReduce, {*G, Table, Arena, GSStack},
-            captureNewHeads());
-
-  EXPECT_THAT(NewHeadResults, testing::UnorderedElementsAre(
+  LRTable Table = LRTable::buildForTests(
+      G->table(), {
+                      {/*State=*/0, id("pointer"), Action::goTo(5)},
+                      {3, tokenSymbol(tok::l_paren),
+                       Action::reduce(/* pointer := class-name */ 0)},
+                      {4, tokenSymbol(tok::l_paren),
+                       Action::reduce(/* pointer := enum-name */ 1)},
+                  });
+  std::vector<const GSS::Node *> Heads = {GSSNode3, GSSNode4};
+  glrReduce(Heads, tokenSymbol(tok::l_paren), {*G, Table, Arena, GSStack});
+
+  EXPECT_THAT(
+      Heads, UnorderedElementsAre(GSSNode3, GSSNode4,
                                   AllOf(state(5), parsedSymbolID(id("pointer")),
                                         parents({GSSNode0}))))
-      << NewHeadResults;
-  EXPECT_EQ(NewHeadResults.front()->Payload->dumpRecursive(*G),
+      << Heads;
+  EXPECT_EQ(Heads.back()->Payload->dumpRecursive(*G),
             "[  0, end) pointer := <ambiguous>\n"
             "[  0, end) ├─pointer := class-name *\n"
             "[  0,   1) │ ├─class-name := <opaque>\n"