diff --git a/src/games/game.h b/src/games/game.h
index cffffebb74..aba2722b21 100644
--- a/src/games/game.h
+++ b/src/games/game.h
@@ -28,7 +28,6 @@
 #include <list>
 #include <memory>
 #include <numeric>
-#include <queue>
 #include <random>
 #include <set>
 #include <stack>
@@ -663,6 +662,8 @@ class GamePlayerRep : public std::enable_shared_from_this<GamePlayerRep> {
   //@}
 };
 
+enum class TraversalOrder { Preorder, Postorder };
+
 /// A node in an extensive game
 class GameNodeRep : public std::enable_shared_from_this<GameNodeRep> {
   friend class GameTreeRep;
@@ -888,8 +889,6 @@ class GameSubgameRep : public std::enable_shared_from_this<GameSubgameRep> {
   InfosetCollection GetSubgameDifference() const;
 };
 
-enum class TraversalOrder { Preorder, Postorder };
-
 class CartesianProductSpace {
 public:
   std::vector<int> m_radices;
@@ -1088,49 +1087,69 @@ class GameRep : public std::enable_shared_from_this<GameRep> {
     class iterator {
       friend class Nodes;
 
-      struct NodeHandler {
-        std::queue<GameNode> m_queue;
-
-        static DFSCallbackResult OnEnter(const GameNode &, int)
-        {
-          return DFSCallbackResult::Continue;
-        }
-        static DFSCallbackResult OnAction(const GameNode &, const GameNode &, int)
-        {
-          return DFSCallbackResult::Continue;
-        }
-        static DFSCallbackResult OnExit(const GameNode &, int)
-        {
-          return DFSCallbackResult::Continue;
-        }
-        void OnVisit(const GameNode &p_node, int) { m_queue.push(p_node); }
+      using ChildIterator = ElementCollection<GameNode, GameNodeRep>::iterator;
+
+      // One frame per node currently open on the path from the root; this mirrors
+      // WalkDFS's own stack, but is kept alive across calls to advance() (instead of
+      // living inside a single call to WalkDFS) so the walk can pause after each node
+      // and resume from exactly where it left off, rather than visiting the whole tree
+      // up front.
+      struct Frame {
+        GameNode m_node;
+        ChildIterator m_current;
+        ChildIterator m_end;
+        bool m_entered{false};
       };
 
       Game m_owner{nullptr};
-      std::shared_ptr<NodeHandler> m_handler;
+      TraversalOrder m_order{TraversalOrder::Preorder};
+      std::stack<Frame> m_stack;
       GameNode m_current{nullptr};
 
-      iterator(const Game &p_game, TraversalOrder p_order)
-        : m_owner(p_game), m_handler(std::make_shared<NodeHandler>())
+      iterator(const Game &p_game, TraversalOrder p_order) : m_owner(p_game), m_order(p_order)
       {
         if (!p_game) {
           m_owner = nullptr;
           return;
         }
-        WalkDFS(p_game, p_game->GetRoot(), p_order, *m_handler);
+        m_stack.push(Frame{p_game->GetRoot(), {}, {}, false});
         advance();
       }
 
       void advance()
       {
-        if (!m_handler || m_handler->m_queue.empty()) {
-          m_current = nullptr;
-          m_owner = nullptr;
-        }
-        else {
-          m_current = m_handler->m_queue.front();
-          m_handler->m_queue.pop();
+        while (!m_stack.empty()) {
+          Frame &f = m_stack.top();
+
+          if (!f.m_entered) {
+            f.m_entered = true;
+            if (!f.m_node->IsTerminal()) {
+              auto children = f.m_node->GetChildren();
+              f.m_current = children.begin();
+              f.m_end = children.end();
+            }
+            if (m_order == TraversalOrder::Preorder) {
+              m_current = f.m_node;
+              return;
+            }
+          }
+
+          if (!f.m_node->IsTerminal() && f.m_current != f.m_end) {
+            GameNode const child = *f.m_current;
+            ++f.m_current;
+            m_stack.push(Frame{child, {}, {}, false});
+            continue;
+          }
+
+          GameNode const finished = f.m_node;
+          m_stack.pop();
+          if (m_order == TraversalOrder::Postorder) {
+            m_current = finished;
+            return;
+          }
         }
+        m_current = nullptr;
+        m_owner = nullptr;
       }
 
     public: