diff --git a/constraint_solver/constraint_solver.h b/constraint_solver/constraint_solver.h
index 4993fdd96f..0440e0519e 100644
--- a/constraint_solver/constraint_solver.h
+++ b/constraint_solver/constraint_solver.h
@@ -227,10 +227,15 @@ struct DefaultPhaseParameters {
   // Seed used to initialize the random part in some heuristics.
   int random_seed;
   // Automatic Restart Size. When diving down, the size of the search
-  // space disminishes. If the current log of the search space is
-  // greater than the the minimal value encountered +
+  // space disminishes. We maintain the minimal log of the size of the search
+  // space with the following behavior:
+  //   - A failure is ignored (no null size).
+  //   - A solution has a size of 1 (and a log of 0).
+  // Then when backtracking, if the current log of the size of the
+  // search space is greater than the minimizal log size recorded +
   // 'restart_log_size', then the search is restarted from scratch. A
-  // parameter < 0 means no restart.
+  // parameter < 0 means no restart. A parameter of 0 indicates that
+  // we restart after each failure.
   double restart_log_size;
 };
 
diff --git a/constraint_solver/default_search.cc b/constraint_solver/default_search.cc
index 61bae66011..e45cf5fbb6 100644
--- a/constraint_solver/default_search.cc
+++ b/constraint_solver/default_search.cc
@@ -516,7 +516,7 @@ class ImpactDecisionBuilder : public DecisionBuilder {
         runner_(NewPermanentCallback(this,
                                      &ImpactDecisionBuilder::RunHeuristics)),
         heuristic_branch_count_(0),
-        min_log_search_space_(std::numeric_limits<double>::max()) {
+        min_log_search_space_(std::numeric_limits<double>::infinity()) {
     CHECK_GE(size_, 0);
     if (size_ > 0) {
       vars_.reset(new IntVar*[size_]);
@@ -663,7 +663,7 @@ class ImpactDecisionBuilder : public DecisionBuilder {
 
   virtual Decision* Next(Solver* const solver) {
     if (!init_done_) {
-      LOG(INFO) << "Init impact based search phase on  " << size_
+      LOG(INFO) << "Init impact based search phase on " << size_
                 << " variables, initialization splits = "
                 << parameters_.initialization_splits
                 << ", heuristic_period = " << parameters_.heuristic_period
@@ -701,7 +701,7 @@ class ImpactDecisionBuilder : public DecisionBuilder {
       } else if (min_log_search_space_ + parameters_.restart_log_size
                  < log_search_space_size) {
         VLOG(2) << "Restarting ";
-        min_log_search_space_ = std::numeric_limits<double>::max();
+        min_log_search_space_ = std::numeric_limits<double>::infinity();
         solver->RestartSearch();
       }
     }
@@ -735,8 +735,13 @@ class ImpactDecisionBuilder : public DecisionBuilder {
           name(heuristic_name),
           runs(heuristic_runs) {}
 
+    // The decision builder we are going to use in this dive.
     DecisionBuilder* const phase;
+    // A name for logging purposes.
     const string name;
+    // How many time we will run this particular heuristic in case the
+    // parameter run_all_heuristics is true. This is useful for random
+    // heuristics where it makes sense to run them more than once.
     const int runs;
   };