Index: dijkstra_shortest_paths.hpp
===================================================================
--- dijkstra_shortest_paths.hpp	(revision 92)
+++ dijkstra_shortest_paths.hpp	(working copy)
@@ -128,21 +128,32 @@
 
       template <class Edge, class Graph>
       void tree_edge(Edge e, Graph& g) {
-        bool decreased = relax(e, g, m_weight, m_predecessor, m_distance,
-                               m_combine, m_compare);
-        if (decreased)
-          m_vis.edge_relaxed(e, g);
-        else
-          m_vis.edge_not_relaxed(e, g);
+        relax_target_confident(e, g, m_weight, m_predecessor, m_distance
+          , m_combine);
+        m_vis.edge_relaxed(e, g);
       }
+     
       template <class Edge, class Graph>
       void gray_target(Edge e, Graph& g) {
+
+#ifdef BOOST_GRAPH_DIJKSTRA_USE_RELAXED_HEAP
         D old_distance = get(m_distance, target(e, g));
+#endif
+#ifdef BOOST_GRAPH_DIJKSTRA_TESTING
+        D old_distance = get(m_distance, target(e, g));
+#endif
 
-        bool decreased = relax(e, g, m_weight, m_predecessor, m_distance,
+         bool decreased = relax_target(e, g, m_weight, m_predecessor, m_distance,
                                m_combine, m_compare);
         if (decreased) {
-          dijkstra_queue_update(m_Q, target(e, g), old_distance);
+
+#ifdef BOOST_GRAPH_DIJKSTRA_USE_RELAXED_HEAP
+        dijkstra_queue_update(m_Q, target(e, g), old_distance);
+#endif
+#ifdef BOOST_GRAPH_DIJKSTRA_TESTING
+        dijkstra_queue_update(m_Q, target(e, g), old_distance);
+#endif
+          m_Q.update(target(e, g));
           m_vis.edge_relaxed(e, g);
         } else
           m_vis.edge_not_relaxed(e, g);
@@ -431,7 +442,7 @@
          choose_param(get_param(params, distance_compare_t()),
                       std::less<D>()),
          choose_param(get_param(params, distance_combine_t()),
-                      closed_plus<D>(inf)),
+                      std::plus<D>()),
          inf,
          choose_param(get_param(params, distance_zero_t()),
                       D()),
Index: relax.hpp
===================================================================
--- relax.hpp	(revision 93)
+++ relax.hpp	(working copy)
@@ -34,6 +34,55 @@
        return a + b;
       }
     };
+
+    template <class Graph, class WeightMap, 
+      class PredecessorMap, class DistanceMap, 
+      class BinaryFunction, class BinaryPredicate>
+    bool relax_target(const typename graph_traits<Graph>::edge_descriptor& e, 
+      const Graph& g, const WeightMap& w, 
+      PredecessorMap& p, DistanceMap& d, 
+      const BinaryFunction& combine, const BinaryPredicate& compare)
+    {
+      typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
+      typedef typename property_traits<DistanceMap>::value_type D;
+      typedef typename property_traits<WeightMap>::value_type W;
+      const Vertex u = source(e, g);
+      const Vertex v = target(e, g);
+      const D& d_u = get(d, u);
+      const D d_v = get(d, v);
+      const W& w_e = get(w, e);
+      
+      // The redundant gets in the return statements are to ensure that extra
+      // floating-point precision in x87 registers does not lead to relax_target()
+      // returning true when the distance did not actually change.
+      if ( compare(combine(d_u, w_e), d_v) ) {
+        put(d, v, combine(d_u, w_e));
+        if(compare(get(d, v), d_v) ) {
+          put(p, v, u);
+          return true;
+        };
+      } 
+      return false;
+    }
+
+    template <class Graph, class WeightMap, class PredecessorMap, class DistanceMap, 
+      class BinaryFunction>
+    void relax_target_confident(
+      const typename graph_traits<Graph>::edge_descriptor& e, 
+      const Graph& g, const WeightMap& w, PredecessorMap& p, DistanceMap& d, 
+      const BinaryFunction& combine)
+    {
+      typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
+      typedef typename property_traits<DistanceMap>::value_type D;
+      typedef typename property_traits<WeightMap>::value_type W;
+      const Vertex u = source(e, g);
+      const Vertex v = target(e, g);
+      const D& d_u = get(d, source(e, g));
+      const W& w_e = get(w, e);
+      
+      put(d, v, combine(d_u, w_e));
+      put(p, v, u);
+    }
     
     template <class Graph, class WeightMap, 
             class PredecessorMap, class DistanceMap,