diff --git a/externs/olx.js b/externs/olx.js
index 33c38bf9cc..42cc2d2a67 100644
--- a/externs/olx.js
+++ b/externs/olx.js
@@ -6479,7 +6479,8 @@ olx.tilegrid;
  *     origins: (Array.<ol.Coordinate>|undefined),
  *     resolutions: !Array.<number>,
  *     tileSize: (number|undefined),
- *     tileSizes: (Array.<number>|undefined)}}
+ *     tileSizes: (Array.<number>|undefined),
+ *     widths: (Array.<number>|undefined)}}
  * @api
  */
 olx.tilegrid.TileGridOptions;
@@ -6535,13 +6536,23 @@ olx.tilegrid.TileGridOptions.prototype.tileSize;
 olx.tilegrid.TileGridOptions.prototype.tileSizes;
 
 
+/**
+ * Widths in tiles. If given, the array length should match the length of the
+ * `resolutions` array, i.e. each resolution will have a number of tile columns.
+ * @type {Array.<number>|undefined}
+ * @api
+ */
+olx.tilegrid.TileGridOptions.prototype.widths;
+
+
 /**
  * @typedef {{origin: (ol.Coordinate|undefined),
  *     origins: (Array.<ol.Coordinate>|undefined),
  *     resolutions: !Array.<number>,
  *     matrixIds: !Array.<string>,
  *     tileSize: (number|undefined),
- *     tileSizes: (Array.<number>|undefined)}}
+ *     tileSizes: (Array.<number>|undefined),
+ *     widths: (Array.<number>|undefined)}}
  * @api
  */
 olx.tilegrid.WMTSOptions;
@@ -6595,6 +6606,15 @@ olx.tilegrid.WMTSOptions.prototype.tileSize;
 olx.tilegrid.WMTSOptions.prototype.tileSizes;
 
 
+/**
+ * Widths in tiles. If given, the array length should match the length of the
+ * `resolutions` array, i.e. each resolution will have a number of tile columns.
+ * @type {Array.<number>|undefined}
+ * @api
+ */
+olx.tilegrid.WMTSOptions.prototype.widths;
+
+
 /**
  * @typedef {{extent: (ol.Extent|undefined),
  *     maxZoom: (number|undefined),
diff --git a/src/ol/attribution.js b/src/ol/attribution.js
index d234c36515..aeeb7bdf12 100644
--- a/src/ol/attribution.js
+++ b/src/ol/attribution.js
@@ -77,8 +77,8 @@ ol.Attribution.prototype.intersectsAnyTileRange =
       if (testTileRange.intersects(tileRange)) {
         return true;
       }
-      var extentTileRange = tileGrid.getTileRangeForExtentAndZ(
-          ol.tilegrid.extentFromProjection(projection), parseInt(zKey, 10));
+      var extentTileRange = tileGrid.getTileRange(
+          parseInt(zKey, 10), projection);
       var width = extentTileRange.getWidth();
       if (tileRange.minX < extentTileRange.minX ||
           tileRange.maxX > extentTileRange.maxX) {
diff --git a/src/ol/source/tilesource.js b/src/ol/source/tilesource.js
index 78c81d8071..bdb602a7d3 100644
--- a/src/ol/source/tilesource.js
+++ b/src/ol/source/tilesource.js
@@ -224,12 +224,11 @@ ol.source.Tile.prototype.getWrapXTileCoord =
     function(tileCoord, opt_projection) {
   var projection = goog.isDef(opt_projection) ?
       opt_projection : this.getProjection();
-  if (goog.isDef(this.wrapX_) && projection.isGlobal()) {
-    var tileGrid = this.getTileGridForProjection(projection);
-    var extent = ol.tilegrid.extentFromProjection(projection);
+  var tileGrid = this.getTileGridForProjection(projection);
+  if (goog.isDef(this.wrapX_) && tileGrid.isGlobal(tileCoord[0], projection)) {
     return this.wrapX_ ?
-        ol.tilecoord.wrapX(tileCoord, tileGrid, extent) :
-        ol.tilecoord.clipX(tileCoord, tileGrid, extent);
+        ol.tilecoord.wrapX(tileCoord, tileGrid, projection) :
+        ol.tilecoord.clipX(tileCoord, tileGrid, projection);
   } else {
     return tileCoord;
   }
diff --git a/src/ol/tilecoord.js b/src/ol/tilecoord.js
index 1ddc43b005..03e451ab94 100644
--- a/src/ol/tilecoord.js
+++ b/src/ol/tilecoord.js
@@ -143,15 +143,15 @@ ol.tilecoord.toString = function(tileCoord) {
 /**
  * @param {ol.TileCoord} tileCoord Tile coordinate.
  * @param {ol.tilegrid.TileGrid} tilegrid Tile grid.
- * @param {ol.Extent} extent Extent.
+ * @param {ol.proj.Projection} projection Projection.
  * @return {ol.TileCoord} Tile coordinate.
  */
 ol.tilecoord.wrapX = (function() {
   var tmpTileCoord = [0, 0, 0];
-  return function(tileCoord, tileGrid, extent) {
+  return function(tileCoord, tileGrid, projection) {
     var z = tileCoord[0];
     var x = tileCoord[1];
-    var tileRange = tileGrid.getTileRangeForExtentAndZ(extent, z);
+    var tileRange = tileGrid.getTileRange(z, projection);
     if (x < tileRange.minX || x > tileRange.maxX) {
       x = goog.math.modulo(x, tileRange.getWidth());
       return ol.tilecoord.createOrUpdate(z, x, tileCoord[2], tmpTileCoord);
@@ -164,11 +164,12 @@ ol.tilecoord.wrapX = (function() {
 /**
  * @param {ol.TileCoord} tileCoord Tile coordinate.
  * @param {ol.tilegrid.TileGrid} tileGrid Tile grid.
- * @param {ol.Extent} extent Extent.
+ * @param {ol.proj.Projection} projection Projection.
  * @return {ol.TileCoord} Tile coordinate.
  */
-ol.tilecoord.clipX = function(tileCoord, tileGrid, extent) {
+ol.tilecoord.clipX = function(tileCoord, tileGrid, projection) {
+  var z = tileCoord[0];
   var x = tileCoord[1];
-  var tileRange = tileGrid.getTileRangeForExtentAndZ(extent, tileCoord[0]);
+  var tileRange = tileGrid.getTileRange(z, projection);
   return (x < tileRange.minX || x > tileRange.maxX) ? null : tileCoord;
 };
diff --git a/src/ol/tilegrid/tilegrid.js b/src/ol/tilegrid/tilegrid.js
index 1e0039770c..8169dc1c06 100644
--- a/src/ol/tilegrid/tilegrid.js
+++ b/src/ol/tilegrid/tilegrid.js
@@ -92,6 +92,16 @@ ol.tilegrid.TileGrid = function(options) {
       (!goog.isDef(this.tileSize_) && !goog.isNull(this.tileSizes_)) ||
       (goog.isDef(this.tileSize_) && goog.isNull(this.tileSizes_)));
 
+  /**
+   * @private
+   * @type {Array.<number>}
+   */
+  this.widths_ = null;
+  if (goog.isDef(options.widths)) {
+    this.widths_ = options.widths;
+    goog.asserts.assert(this.widths_.length == this.resolutions_.length);
+  }
+
 };
 
 
@@ -373,6 +383,25 @@ ol.tilegrid.TileGrid.prototype.getTileCoordResolution = function(tileCoord) {
 };
 
 
+/**
+ * @param {number} z Zoom level.
+ * @param {ol.proj.Projection} projection Projection.
+ * @param {ol.TileRange=} opt_tileRange Tile range.
+ * @return {ol.TileRange} Tile range.
+ */
+ol.tilegrid.TileGrid.prototype.getTileRange =
+    function(z, projection, opt_tileRange) {
+  var projectionExtentTileRange = this.getTileRangeForExtentAndZ(
+      ol.tilegrid.extentFromProjection(projection), z);
+  var width = this.getWidth(z);
+  if (!goog.isDef(width)) {
+    width = projectionExtentTileRange.getWidth();
+  }
+  return ol.TileRange.createOrUpdate(
+      0, width - 1, 0, projectionExtentTileRange.getHeight(), opt_tileRange);
+};
+
+
 /**
  * @param {number} z Z.
  * @return {number} Tile size.
@@ -389,6 +418,19 @@ ol.tilegrid.TileGrid.prototype.getTileSize = function(z) {
 };
 
 
+/**
+ * @param {number} z Zoom level.
+ * @return {number|undefined} Width for the specified zoom level or `undefined`
+ *     if unknown.
+ */
+ol.tilegrid.TileGrid.prototype.getWidth = function(z) {
+  if (!goog.isNull(this.widths_)) {
+    goog.asserts.assert(this.minZoom <= z && z <= this.maxZoom);
+    return this.widths_[z];
+  }
+};
+
+
 /**
  * @param {number} resolution Resolution.
  * @return {number} Z.
@@ -399,6 +441,26 @@ ol.tilegrid.TileGrid.prototype.getZForResolution = function(resolution) {
 };
 
 
+/**
+ * @param {number} z Zoom level.
+ * @param {ol.proj.Projection} projection Projection.
+ * @return {boolean} Whether the tile grid is defined for the whole globe when
+ *     used with the provided `projection` at zoom level `z`.
+ */
+ol.tilegrid.TileGrid.prototype.isGlobal = function(z, projection) {
+  var width = this.getWidth(z);
+  if (goog.isDef(width)) {
+    var projTileGrid = ol.tilegrid.getForProjection(projection);
+    var projExtent = projection.getExtent();
+    return this.getTileSize(z) * width ==
+        projTileGrid.getTileSize(z) *
+        projTileGrid.getTileRangeForExtentAndZ(projExtent, z).getWidth();
+  } else {
+    return projection.isGlobal();
+  }
+};
+
+
 /**
  * @param {ol.proj.Projection} projection Projection.
  * @return {ol.tilegrid.TileGrid} Default tile grid for the passed projection.
@@ -433,10 +495,17 @@ ol.tilegrid.createForExtent =
   var resolutions = ol.tilegrid.resolutionsFromExtent(
       extent, opt_maxZoom, tileSize);
 
+  var widths = new Array(resolutions.length);
+  var extentWidth = ol.extent.getWidth(extent);
+  for (var z = resolutions.length - 1; z >= 0; --z) {
+    widths[z] = extentWidth / tileSize / resolutions[z];
+  }
+
   return new ol.tilegrid.TileGrid({
     origin: ol.extent.getCorner(extent, corner),
     resolutions: resolutions,
-    tileSize: tileSize
+    tileSize: tileSize,
+    widths: widths
   });
 };
 
diff --git a/src/ol/tilegrid/wmtstilegrid.js b/src/ol/tilegrid/wmtstilegrid.js
index 228d25715a..9f381c1682 100644
--- a/src/ol/tilegrid/wmtstilegrid.js
+++ b/src/ol/tilegrid/wmtstilegrid.js
@@ -34,7 +34,8 @@ ol.tilegrid.WMTS = function(options) {
     origins: options.origins,
     resolutions: options.resolutions,
     tileSize: options.tileSize,
-    tileSizes: options.tileSizes
+    tileSizes: options.tileSizes,
+    widths: options.widths
   });
 
 };
@@ -77,6 +78,8 @@ ol.tilegrid.WMTS.createFromCapabilitiesMatrixSet =
   var origins = [];
   /** @type {!Array.<number>} */
   var tileSizes = [];
+  /** @type {!Array.<number>} */
+  var widths = [];
 
   var supportedCRSPropName = 'SupportedCRS';
   var matrixIdsPropName = 'TileMatrix';
@@ -112,12 +115,14 @@ ol.tilegrid.WMTS.createFromCapabilitiesMatrixSet =
         var tileHeight = elt[tileHeightPropName];
         goog.asserts.assert(tileWidth == tileHeight);
         tileSizes.push(tileWidth);
+        widths.push(elt['MatrixWidth']);
       });
 
   return new ol.tilegrid.WMTS({
     origins: origins,
     resolutions: resolutions,
     matrixIds: matrixIds,
-    tileSizes: tileSizes
+    tileSizes: tileSizes,
+    widths: widths
   });
 };