diff --git a/src/search.cpp b/src/search.cpp
index ab58ca64..65ed9b73 100644
--- a/src/search.cpp
+++ b/src/search.cpp
@@ -565,6 +565,7 @@ namespace {
 
     constexpr bool PvNode = NT == PV;
     const bool rootNode = PvNode && ss->ply == 0;
+    const Depth maxNextDepth = rootNode ? depth : depth + 1;
 
     // Check if we have an upcoming move which draws by repetition, or
     // if the opponent had an alternative move earlier to this position.
@@ -1259,7 +1260,8 @@ moves_loop: // When in check, search starts from here
           (ss+1)->pv = pv;
           (ss+1)->pv[0] = MOVE_NONE;
 
-          value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
+          value = -search<PV>(pos, ss+1, -beta, -alpha,
+                              std::min(maxNextDepth, newDepth), false);
       }
 
       // Step 18. Undo move
diff --git a/src/timeman.cpp b/src/timeman.cpp
index 6d9c95ef..da08f12d 100644
--- a/src/timeman.cpp
+++ b/src/timeman.cpp
@@ -75,7 +75,7 @@ void TimeManagement::init(Search::LimitsType& limits, Color us, int ply) {
   // game time for the current move, so also cap to 20% of available game time.
   if (limits.movestogo == 0)
   {
-      optScale = std::min(0.008 + std::pow(ply + 3.0, 0.5) / 250.0,
+      optScale = std::min(0.0084 + std::pow(ply + 3.0, 0.5) * 0.0042,
                            0.2 * limits.time[us] / double(timeLeft));
       maxScale = std::min(7.0, 4.0 + ply / 12.0);
   }