diff --git a/python/mwmatching.py b/python/mwmatching.py
index 492fc3d..37caf24 100644
--- a/python/mwmatching.py
+++ b/python/mwmatching.py
@@ -613,7 +613,24 @@ class _MatchingContext:
             blossom.vertex_set.clear()
             del blossom.vertex_set
 
-    def edge_slack_2x_info(
+    def edge_pseudo_slack_2x(self, e: int) -> float:
+        """Return 2 times the pseudo-slack of the specified edge.
+
+        The pseudo-slack of an edge ignores pending changes to vertex duals.
+
+        For an edge between two S-vertices (in different top-level blossoms),
+        the true slack is the pseudo-slack minus 2 times the running sum
+        of delta steps.
+
+        For an edge between an S-vertex and unlabeled vertex,
+        the true slack is the pseudo-slack minus the running sum of delta
+        steps, plus the pending offset of the top-level blossom that contains
+        the unlabeled vertex.
+        """
+        (x, y, w) = self.graph.edges[e]
+        return self.vertex_dual_2x[x] + self.vertex_dual_2x[y] - 2 * w
+
+    def edge_slack_2x(
             self,
             x: int,
             y: int,
@@ -645,13 +662,6 @@ class _MatchingContext:
         dual_2x += by.vertex_dual_offset
         return dual_2x - 2 * w
 
-    def edge_slack_2x(self, e: int) -> float:
-        """Return 2 times the slack of the edge with index "e"."""
-        (x, y, w) = self.graph.edges[e]
-        bx = self.vertex_set_node[x].find()
-        by = self.vertex_set_node[y].find()
-        return self.edge_slack_2x_info(x, y, bx, by, w)
-
     #
     # Least-slack edge tracking:
     #
@@ -689,36 +699,26 @@ class _MatchingContext:
         for blossom in self.trivial_blossom + self.nontrivial_blossom:
             blossom.delta2_node = None
 
-    def lset_add_vertex_edge(
-            self,
-            y: int,
-            by: _Blossom,
-            e: int,
-            slack: float
-            ) -> None:
+    def lset_add_vertex_edge(self, y: int, by: _Blossom, e: int) -> None:
         """Add edge "e" from an S-vertex to unlabeled vertex or T-vertex "y".
 
         This function takes time O(log(n)).
         """
-
-        # TODO -- Simplify: We don't need to know the true slack of the edge,
-        #            only the pseudo-slack based on raw vertex duals and weight.
+        prio = self.edge_pseudo_slack_2x(e)
 
         best_edge = self.vertex_best_edge[y]
         if best_edge != -1:
-            best_slack = self.edge_slack_2x(best_edge)
-            if slack >= best_slack:
+            best_prio = self.edge_pseudo_slack_2x(best_edge)
+            if prio >= best_prio:
                 return
 
         self.vertex_best_edge[y] = e
 
-        (p, q, w) = self.graph.edges[e]
-        prio = self.vertex_dual_2x[p] + self.vertex_dual_2x[q] - 2 * w
         prev_min = by.vertex_set.min_prio()
         self.vertex_set_node[y].set_prio(prio)
 
         if (by.label == _LABEL_NONE) and (prio < prev_min):
-            prio = slack + self.delta_sum_2x
+            prio += by.vertex_dual_offset
             if by.delta2_node is None:
                 by.delta2_node = self.delta2_queue.insert(prio, by)
             elif prio < by.delta2_node.prio:
@@ -1476,7 +1476,7 @@ class _MatchingContext:
 
                 # Check whether this edge is tight (has zero slack).
                 # Only tight edges may be part of an alternating tree.
-                slack = self.edge_slack_2x_info(x, y, bx, by, w)
+                slack = self.edge_slack_2x(x, y, bx, by, w)
                 if slack <= 0:
                     if ylabel == _LABEL_NONE:
                         # Assign label T to the blossom that contains "y".
@@ -1509,7 +1509,7 @@ class _MatchingContext:
                     # any S-vertex. We do this for T-vertices and unlabeled
                     # vertices. Edges which already have zero slack are still
                     # tracked.
-                    self.lset_add_vertex_edge(y, by, e, slack)
+                    self.lset_add_vertex_edge(y, by, e)
 
         # No further S vertices to scan, and no augmenting path found.
         return None