diff --git a/src/ol/dom/tilelayerrenderer.js b/src/ol/dom/tilelayerrenderer.js
index 1a49082e78..2984db6757 100644
--- a/src/ol/dom/tilelayerrenderer.js
+++ b/src/ol/dom/tilelayerrenderer.js
@@ -135,3 +135,39 @@ ol.dom.TileLayerRenderer.prototype.removeInvisibleTiles_ = function(
     }
   }
 };
+
+
+/**
+ * Get the best/preferred z for an arbitrary resolution.
+ * @private
+ * @param {number} resolution Resolution.
+ * @return {number} Z.
+ * TODO: this should probably be shared with the WebGL TileLayerRenderer,
+ * but our current class hierarchy does not allow this sharing.
+*/
+ol.dom.TileLayerRenderer.prototype.getPreferredZ_ = (function() {
+  var cache = {};
+  return function(resolution) {
+    if (resolution in cache) {
+      return cache[resolution];
+    }
+    var tileLayer = /** @type {ol.TileLayer} */ (this.getLayer());
+    var tileStore = tileLayer.getStore();
+    var tileGrid = tileStore.getTileGrid();
+    var gridResolutions = tileGrid.getResolutions();
+    var minDiff = Number.POSITIVE_INFINITY;
+    var candidate, diff, z, r;
+    for (var i = 0, ii = gridResolutions.length; i < ii; ++i) {
+      // assumes sorted resolutions
+      diff = Math.abs(resolution - gridResolutions[i]);
+      if (diff < minDiff) {
+        z = i;
+        minDiff = diff;
+      } else {
+        break;
+      }
+    }
+    cache[resolution] = z;
+    return z;
+  };
+})();
diff --git a/src/ol/dom/tilelayerrenderer_test.js b/src/ol/dom/tilelayerrenderer_test.js
new file mode 100644
index 0000000000..36f01d2eff
--- /dev/null
+++ b/src/ol/dom/tilelayerrenderer_test.js
@@ -0,0 +1,73 @@
+goog.require('goog.dom');
+goog.require('goog.dom.TagName');
+goog.require('goog.testing.jsunit');
+goog.require('ol.Coordinate');
+goog.require('ol.Extent');
+goog.require('ol.Projection');
+goog.require('ol.TileGrid');
+goog.require('ol.TileLayer');
+goog.require('ol.TileStore');
+goog.require('ol.TileUrlFunction');
+goog.require('ol.dom.Map');
+goog.require('ol.dom.TileLayerRenderer');
+
+
+var tileLayerRenderer;
+
+
+function setUp() {
+  var map = new ol.dom.Map(
+      goog.dom.createElement(goog.dom.TagName.DIV));
+
+  var resolutions = [100, 80, 50, 10, 1, 0.1];
+  var extent = new ol.Extent(0, 0, 100000, 100000);
+  var origin = new ol.Coordinate(0, 0);
+  var tileGrid = new ol.TileGrid(resolutions, extent, origin);
+
+  var projection = ol.Projection.getFromCode('EPSG:3857');
+  var tileUrlFunction = ol.TileUrlFunction.createFromTemplate('{z}/{x}/{y}');
+  var tileStore = new ol.TileStore(projection, tileGrid, tileUrlFunction);
+
+  var tileLayer = new ol.TileLayer(tileStore);
+
+  tileLayerRenderer = new ol.dom.TileLayerRenderer(
+      map, tileLayer,
+      goog.dom.createElement(goog.dom.TagName.DIV));
+}
+
+
+function testGetPreferredZ() {
+
+  var z;
+
+  // gets the max resolution.
+  z = tileLayerRenderer.getPreferredZ_(100);
+  assertEquals(0, z);
+
+  // gets the min resolution.
+  z = tileLayerRenderer.getPreferredZ_(0.1);
+  assertEquals(5, z);
+
+  // gets the max when bigger.
+  z = tileLayerRenderer.getPreferredZ_(200);
+  assertEquals(0, z);
+
+  // gets the min when smaller.
+  z = tileLayerRenderer.getPreferredZ_(0.01);
+  assertEquals(5, z);
+
+  // gets the first when in the middle.
+  z = tileLayerRenderer.getPreferredZ_(90);
+  assertEquals(0, z);
+
+  // gets the closer when elsewhere.
+
+  z = tileLayerRenderer.getPreferredZ_(89);
+  assertEquals(1, z);
+
+  z = tileLayerRenderer.getPreferredZ_(49);
+  assertEquals(2, z);
+
+  z = tileLayerRenderer.getPreferredZ_(0.5);
+  assertEquals(5, z);
+}