diff --git a/src/ol/source/wmtssource.js b/src/ol/source/wmtssource.js
index 7eb25cdb2b..d815e849b1 100644
--- a/src/ol/source/wmtssource.js
+++ b/src/ol/source/wmtssource.js
@@ -355,7 +355,7 @@ ol.source.WMTS.optionsFromCapabilities = function(wmtsCap, config) {
 
   goog.asserts.assert(l['TileMatrixSetLink'].length > 0,
       'layer has TileMatrixSetLink');
-  var idx, matrixSet, wrapX;
+  var idx, matrixSet;
   if (l['TileMatrixSetLink'].length > 1) {
     idx = goog.array.findIndex(l['TileMatrixSetLink'],
         function(elt, index, array) {
@@ -380,13 +380,6 @@ ol.source.WMTS.optionsFromCapabilities = function(wmtsCap, config) {
   goog.asserts.assert(!goog.isNull(matrixSet),
       'TileMatrixSet must not be null');
 
-  var wgs84BoundingBox = l['WGS84BoundingBox'];
-  if (goog.isDef(wgs84BoundingBox)) {
-    var wgs84ProjectionExtent = ol.proj.get('EPSG:4326').getExtent();
-    wrapX = (wgs84BoundingBox[0] == wgs84ProjectionExtent[0] &&
-        wgs84BoundingBox[2] == wgs84ProjectionExtent[2]);
-  }
-
   var format = /** @type {string} */ (l['Format'][0]);
   if (goog.isDef(config['format'])) {
     format = config['format'];
@@ -434,16 +427,24 @@ ol.source.WMTS.optionsFromCapabilities = function(wmtsCap, config) {
         /urn:ogc:def:crs:(\w+):(.*:)?(\w+)$/, '$1:$3'));
   }
 
-  var projectionExtent = projection.getExtent();
-  var extent;
-  if (!goog.isNull(projectionExtent)) {
-    var projectionExtentWgs84 = ol.proj.transformExtent(
-        projectionExtent, projection, 'EPSG:4326');
-    if (ol.extent.containsExtent(projectionExtentWgs84, wgs84BoundingBox)) {
-      extent = ol.proj.transformExtent(
-          wgs84BoundingBox, 'EPSG:4326', projection);
+  var wgs84BoundingBox = l['WGS84BoundingBox'];
+  var extent, wrapX;
+  if (goog.isDef(wgs84BoundingBox)) {
+    var wgs84ProjectionExtent = ol.proj.get('EPSG:4326').getExtent();
+    wrapX = (wgs84BoundingBox[0] == wgs84ProjectionExtent[0] &&
+        wgs84BoundingBox[2] == wgs84ProjectionExtent[2]);
+    extent = ol.proj.transformExtent(
+        wgs84BoundingBox, 'EPSG:4326', projection);
+    var projectionExtent = projection.getExtent();
+    if (!goog.isNull(projectionExtent)) {
+      // If possible, do a sanity check on the extent - it should never be
+      // bigger than the validity extent of the projection of a matrix set.
+      if (!ol.extent.containsExtent(projectionExtent, extent)) {
+        extent = undefined;
+      }
     }
   }
+
   var tileGrid = ol.tilegrid.WMTS.createFromCapabilitiesMatrixSet(
       matrixSetObj, extent);