diff --git a/cpp/mwmatching.h b/cpp/mwmatching.h
index 3d777f8..84455a9 100644
--- a/cpp/mwmatching.h
+++ b/cpp/mwmatching.h
@@ -1414,7 +1414,7 @@ public:
             assert(sub_blossom->vertex_dual_offset == 0);
             sub_blossom->vertex_dual_offset = vertex_dual_offset;
 
-            // Add unlabeled blossom to the delta2 queue.
+            // Add unlabeled sub-blossom to the delta2 queue.
             delta2_enable_blossom(sub_blossom);
         }
 
@@ -1423,65 +1423,53 @@ public:
         // that ran through this blossom by linking some of the sub-blossoms
         // into the tree.
 
-        // Find the sub-blossom that was attached to the parent node
-        // in the alternating tree.
+        // Find the sub-blossom through which the expanding blossom was
+        // attached to the alternating tree.
         BlossomT* entry = top_level_blossom(blossom->tree_edge.second);
 
-        // Assign label T to that blossom and link to the alternating tree.
-        assign_blossom_label_t(entry);
-        entry->tree_edge = blossom->tree_edge;
-        entry->tree_root = blossom->tree_root;
-
         // Find the position of this sub-blossom within the expanding blossom.
         auto subblossom_loc = blossom->find_subblossom(entry);
         VertexId entry_pos = subblossom_loc.first;
         auto entry_it = subblossom_loc.second;
 
-        // Walk around the blossom from "entry" to the base
+        // Get the edge that attaches this blossom to the alternating tree.
+        VertexId x, y;
+        std::tie(x, y) = blossom->tree_edge;
+
+        // Walk around the expanding blossom from "entry" to its base
         // in an even number of steps.
+        auto sub_begin = blossom->subblossoms.begin();
+        auto sub_end = blossom->subblossoms.end();
         auto sub_it = entry_it;
-        if (entry_pos % 2 == 0) {
+        while ((sub_it != sub_begin) && (sub_it != sub_end)) {
 
-            // Walk backward to the base.
-            auto sub_begin = blossom->subblossoms.begin();
-            while (sub_it != sub_begin) {
-                // Assign label S to the next node on the path.
+            // Assign label T to the current sub-blossom on the path.
+            // This also assigns label S to the next sub-blossom.
+            extend_tree_s_to_t(x, y);
+
+            if (entry_pos % 2 == 0) {
+                // Walk two steps backward to the base.
                 --sub_it;
-                extend_tree_t_to_s(sub_it->edge.first);
-
-                // Assign label T to the next node on the path.
                 assert(sub_it != sub_begin);
                 --sub_it;
-                BlossomT* sub_blossom = sub_it->blossom;
-                assign_blossom_label_t(sub_blossom);
-                sub_blossom->tree_edge = flip_vertex_pair(sub_it->edge);
-                sub_blossom->tree_root = blossom->tree_root;
-            }
-
-        } else {
-
-            // Walk forward to the base.
-            auto sub_end = blossom->subblossoms.end();
-            while (sub_it != sub_end) {
-                // Assign label S to the next node on the path.
-                extend_tree_t_to_s(sub_it->edge.second);
+                // Get the edge from S-sub-blossom to next sub-blossom.
+                std::tie(y, x) = sub_it->edge;
+            } else {
+                // Walk two steps forward to the base.
                 ++sub_it;
-
-                // Assign label T to the next node on the path.
-                // We may wrap past the end of the subblossom list.
                 assert(sub_it != sub_end);
-                VertexPair& tree_edge = sub_it->edge;
+                // Get the edge from S-sub-blossom to next sub-blossom.
+                std::tie(x, y) = sub_it->edge;
                 ++sub_it;
-
-                BlossomT *sub_blossom = (sub_it == sub_end) ?
-                    blossom->subblossoms.front().blossom :
-                    sub_it->blossom;
-                assign_blossom_label_t(sub_blossom);
-                sub_blossom->tree_edge = tree_edge;
-                sub_blossom->tree_root = blossom->tree_root;
             }
         }
 
+        // Finally, assign label T to the base sub-blossom.
+        BlossomT* base = blossom->subblossoms.front().blossom;
+        assign_blossom_label_t(base);
+        base->tree_edge = std::make_pair(x, y);
+        base->tree_root = blossom->tree_root;
+
         // Delete the expanded blossom.
         nontrivial_blossom.erase(blossom->this_blossom_iterator);
     }
@@ -1655,34 +1643,6 @@ public:
 
     /* **********  Alternating tree:  ********** */
 
-    /**
-     * Assign label S to the unlabeled blossom that contains vertex "x".
-     *
-     * The newly labeled S-blossom is added to the alternating tree
-     * via its matched edge. All vertices in the newly labeled S-blossom
-     * are added to the scan queue.
-     *
-     * @pre "x" is an unlabeled vertex.
-     * @pre "x" is matched to a T-vertex via a tight edge.
-     */
-    void extend_tree_t_to_s(VertexId x)
-    {
-        // Assign label S to the blossom that contains vertex "x".
-        BlossomT* bx = top_level_blossom(x);
-        assign_blossom_label_s(bx);
-
-        // Vertex "x" is matched to T-vertex "y".
-        VertexId y = vertex_mate[x];
-        assert(y != NO_VERTEX);
-
-        BlossomT* by = top_level_blossom(y);
-        assert(by->label == LABEL_T);
-
-        // Attach the blossom to the alternating tree via vertex "y".
-        bx->tree_edge = std::make_pair(y, x);
-        bx->tree_root = by->tree_root;
-    }
-
     /**
      * Assign label T to the unlabeled blossom that contains vertex "y".
      *
@@ -1708,9 +1668,14 @@ public:
         by->tree_root = bx->tree_root;
 
         // Assign label S to the blossom that is mated to the T-blossom.
-        VertexId z = vertex_mate[by->base_vertex];
+        VertexId y2 = by->base_vertex;
+        VertexId z = vertex_mate[y2];
         assert(z != NO_VERTEX);
-        extend_tree_t_to_s(z);
+
+        BlossomT* bz = top_level_blossom(z);
+        assign_blossom_label_s(bz);
+        bz->tree_edge = std::make_pair(y2, z);
+        bz->tree_root = by->tree_root;
     }
 
     /**