diff --git a/cpp/mwmatching.h b/cpp/mwmatching.h
index cad8d19..a98bc7f 100644
--- a/cpp/mwmatching.h
+++ b/cpp/mwmatching.h
@@ -1862,7 +1862,7 @@ public:
      * thereby increasing the number of matched edges by 1.
      * If no such path is found, the matching must already be optimal.
      *
-     * This function takes time O(n**2).
+     * This function takes time O((n + m) * log(n)).
      *
      * @return True if the matching was successfully augmented;
      *         false if no further improvement is possible.
@@ -1995,7 +1995,7 @@ public:
         // of matched edges by 1.
         //
         // This loop runs through at most (n/2 + 1) iterations.
-        // Each iteration takes time O(n**2).
+        // Each iteration takes time O((n + m) * log(n)).
         while (run_stage()) ;
 
         // Clean up and unwind lazy updates to dual variables.
@@ -2357,12 +2357,12 @@ private:
  * no effect on the maximum-weight matching.
  * Edges with negative weight are ignored.
  *
- * This function takes time O(n**3), where "n" is the number of vertices.
- * This function uses O(n + m) memory, where "m" is the number of edges.
+ * This function takes time O(n * (n + m) * log(n)),
+ * where "n" is the number of vertices and "m" is the number of edges.
+ * This function uses O(n + m) memory.
  *
  * @tparam WeightType   Type used to represent edge weights.
- *                      This must be a signed type.
- *                      For example "long" or "double".
+ *                      This must be a signed type, e.g. "long" or "double".
  *
  * @param  edges        Graph defined as a vector of weighted edges.
  *