diff --git a/lib/OpenLayers/Tile.js b/lib/OpenLayers/Tile.js
index aa3b89b1ee..fb8b08d931 100644
--- a/lib/OpenLayers/Tile.js
+++ b/lib/OpenLayers/Tile.js
@@ -195,8 +195,12 @@ OpenLayers.Tile = OpenLayers.Class({
     setBounds: function(bounds) {
         bounds = bounds.clone();
         if (this.layer.map.baseLayer.wrapDateLine) {
-            var worldExtent = this.layer.map.getMaxExtent();
-            bounds = bounds.wrapDateLine(worldExtent);
+            var worldExtent = this.layer.map.getMaxExtent(),
+                tolerance = this.layer.map.getResolution();
+            bounds = bounds.wrapDateLine(worldExtent, {
+                leftTolerance: tolerance,
+                rightTolerance: tolerance
+            });
         }
         this.bounds = bounds;
     },