diff --git a/src/ol/source/TileArcGISRest.js b/src/ol/source/TileArcGISRest.js
index 6d4a0613e9..471042e227 100644
--- a/src/ol/source/TileArcGISRest.js
+++ b/src/ol/source/TileArcGISRest.js
@@ -76,6 +76,7 @@ class TileArcGISRest extends TileImage {
       reprojectionErrorThreshold: options.reprojectionErrorThreshold,
       tileGrid: options.tileGrid,
       tileLoadFunction: options.tileLoadFunction,
+      tileUrlFunction: tileUrlFunction,
       url: options.url,
       urls: options.urls,
       wrapX: options.wrapX !== undefined ? options.wrapX : true,
@@ -169,41 +170,6 @@ class TileArcGISRest extends TileImage {
     return /** @type {number} */ (pixelRatio);
   }
 
-  /**
-   * @inheritDoc
-   */
-  fixedTileUrlFunction(tileCoord, pixelRatio, projection) {
-
-    let tileGrid = this.getTileGrid();
-    if (!tileGrid) {
-      tileGrid = this.getTileGridForProjection(projection);
-    }
-
-    if (tileGrid.getResolutions().length <= tileCoord[0]) {
-      return undefined;
-    }
-
-    const tileExtent = tileGrid.getTileCoordExtent(
-      tileCoord, this.tmpExtent_);
-    let tileSize = toSize(
-      tileGrid.getTileSize(tileCoord[0]), this.tmpSize);
-
-    if (pixelRatio != 1) {
-      tileSize = scaleSize(tileSize, pixelRatio, this.tmpSize);
-    }
-
-    // Apply default params and override with user specified values.
-    const baseParams = {
-      'F': 'image',
-      'FORMAT': 'PNG32',
-      'TRANSPARENT': true
-    };
-    assign(baseParams, this.params_);
-
-    return this.getRequestUrl_(tileCoord, tileSize, tileExtent,
-      pixelRatio, projection, baseParams);
-  }
-
   /**
    * Update the user-provided params.
    * @param {Object} params Params.
@@ -215,5 +181,44 @@ class TileArcGISRest extends TileImage {
   }
 }
 
+/**
+ * @param {import("../tilecoord.js").TileCoord} tileCoord The tile coordinate
+ * @param {number} pixelRatio The pixel ratio
+ * @param {import("../proj/Projection.js").default} projection The projection
+ * @return {string|undefined} The tile URL
+ * @this {TileArcGISRest}
+ */
+function tileUrlFunction(tileCoord, pixelRatio, projection) {
+
+  let tileGrid = this.getTileGrid();
+  if (!tileGrid) {
+    tileGrid = this.getTileGridForProjection(projection);
+  }
+
+  if (tileGrid.getResolutions().length <= tileCoord[0]) {
+    return undefined;
+  }
+
+  const tileExtent = tileGrid.getTileCoordExtent(
+    tileCoord, this.tmpExtent_);
+  let tileSize = toSize(
+    tileGrid.getTileSize(tileCoord[0]), this.tmpSize);
+
+  if (pixelRatio != 1) {
+    tileSize = scaleSize(tileSize, pixelRatio, this.tmpSize);
+  }
+
+  // Apply default params and override with user specified values.
+  const baseParams = {
+    'F': 'image',
+    'FORMAT': 'PNG32',
+    'TRANSPARENT': true
+  };
+  assign(baseParams, this.params_);
+
+  return this.getRequestUrl_(tileCoord, tileSize, tileExtent,
+    pixelRatio, projection, baseParams);
+}
+
 
 export default TileArcGISRest;
diff --git a/src/ol/source/TileWMS.js b/src/ol/source/TileWMS.js
index 4c6760b6a6..a69f5518e8 100644
--- a/src/ol/source/TileWMS.js
+++ b/src/ol/source/TileWMS.js
@@ -98,6 +98,7 @@ class TileWMS extends TileImage {
       tileClass: options.tileClass,
       tileGrid: options.tileGrid,
       tileLoadFunction: options.tileLoadFunction,
+      tileUrlFunction: tileUrlFunction,
       url: options.url,
       urls: options.urls,
       wrapX: options.wrapX !== undefined ? options.wrapX : true,
@@ -321,52 +322,6 @@ class TileWMS extends TileImage {
     return res.join('/');
   }
 
-  /**
-   * @inheritDoc
-   */
-  fixedTileUrlFunction(tileCoord, pixelRatio, projection) {
-
-    let tileGrid = this.getTileGrid();
-    if (!tileGrid) {
-      tileGrid = this.getTileGridForProjection(projection);
-    }
-
-    if (tileGrid.getResolutions().length <= tileCoord[0]) {
-      return undefined;
-    }
-
-    if (pixelRatio != 1 && (!this.hidpi_ || this.serverType_ === undefined)) {
-      pixelRatio = 1;
-    }
-
-    const tileResolution = tileGrid.getResolution(tileCoord[0]);
-    let tileExtent = tileGrid.getTileCoordExtent(tileCoord, this.tmpExtent_);
-    let tileSize = toSize(
-      tileGrid.getTileSize(tileCoord[0]), this.tmpSize);
-
-    const gutter = this.gutter_;
-    if (gutter !== 0) {
-      tileSize = bufferSize(tileSize, gutter, this.tmpSize);
-      tileExtent = buffer(tileExtent, tileResolution * gutter, tileExtent);
-    }
-
-    if (pixelRatio != 1) {
-      tileSize = scaleSize(tileSize, pixelRatio, this.tmpSize);
-    }
-
-    const baseParams = {
-      'SERVICE': 'WMS',
-      'VERSION': DEFAULT_WMS_VERSION,
-      'REQUEST': 'GetMap',
-      'FORMAT': 'image/png',
-      'TRANSPARENT': true
-    };
-    assign(baseParams, this.params_);
-
-    return this.getRequestUrl_(tileCoord, tileSize, tileExtent,
-      pixelRatio, projection, baseParams);
-  }
-
   /**
    * Update the user-provided params.
    * @param {Object} params Params.
@@ -387,5 +342,55 @@ class TileWMS extends TileImage {
   }
 }
 
+/**
+ * @param {import("../tilecoord.js").TileCoord} tileCoord The tile coordinate
+ * @param {number} pixelRatio The pixel ratio
+ * @param {import("../proj/Projection.js").default} projection The projection
+ * @return {string|undefined} The tile URL
+ * @this {TileWMS}
+ */
+function tileUrlFunction(tileCoord, pixelRatio, projection) {
+
+  let tileGrid = this.getTileGrid();
+  if (!tileGrid) {
+    tileGrid = this.getTileGridForProjection(projection);
+  }
+
+  if (tileGrid.getResolutions().length <= tileCoord[0]) {
+    return undefined;
+  }
+
+  if (pixelRatio != 1 && (!this.hidpi_ || this.serverType_ === undefined)) {
+    pixelRatio = 1;
+  }
+
+  const tileResolution = tileGrid.getResolution(tileCoord[0]);
+  let tileExtent = tileGrid.getTileCoordExtent(tileCoord, this.tmpExtent_);
+  let tileSize = toSize(
+    tileGrid.getTileSize(tileCoord[0]), this.tmpSize);
+
+  const gutter = this.gutter_;
+  if (gutter !== 0) {
+    tileSize = bufferSize(tileSize, gutter, this.tmpSize);
+    tileExtent = buffer(tileExtent, tileResolution * gutter, tileExtent);
+  }
+
+  if (pixelRatio != 1) {
+    tileSize = scaleSize(tileSize, pixelRatio, this.tmpSize);
+  }
+
+  const baseParams = {
+    'SERVICE': 'WMS',
+    'VERSION': DEFAULT_WMS_VERSION,
+    'REQUEST': 'GetMap',
+    'FORMAT': 'image/png',
+    'TRANSPARENT': true
+  };
+  assign(baseParams, this.params_);
+
+  return this.getRequestUrl_(tileCoord, tileSize, tileExtent,
+    pixelRatio, projection, baseParams);
+}
+
 
 export default TileWMS;
diff --git a/src/ol/source/UrlTile.js b/src/ol/source/UrlTile.js
index 548e30bddf..0a2c02d311 100644
--- a/src/ol/source/UrlTile.js
+++ b/src/ol/source/UrlTile.js
@@ -50,6 +50,12 @@ class UrlTile extends TileSource {
       transition: options.transition
     });
 
+    /**
+     * @private
+     * @type {boolean}
+     */
+    this.generateTileUrlFunction_ = !options.tileUrlFunction;
+
     /**
      * @protected
      * @type {import("../Tile.js").LoadFunction}
@@ -60,8 +66,7 @@ class UrlTile extends TileSource {
      * @protected
      * @type {import("../Tile.js").UrlFunction}
      */
-    this.tileUrlFunction = this.fixedTileUrlFunction ?
-      this.fixedTileUrlFunction.bind(this) : nullTileUrlFunction;
+    this.tileUrlFunction = options.tileUrlFunction ? options.tileUrlFunction.bind(this) : nullTileUrlFunction;
 
     /**
      * @protected
@@ -74,9 +79,6 @@ class UrlTile extends TileSource {
     } else if (options.url) {
       this.setUrl(options.url);
     }
-    if (options.tileUrlFunction) {
-      this.setTileUrlFunction(options.tileUrlFunction);
-    }
 
     /**
      * @private
@@ -173,9 +175,7 @@ class UrlTile extends TileSource {
    */
   setUrl(url) {
     const urls = this.urls = expandUrl(url);
-    this.setTileUrlFunction(this.fixedTileUrlFunction ?
-      this.fixedTileUrlFunction.bind(this) :
-      createFromTemplates(urls, this.tileGrid), url);
+    this.setUrls(urls);
   }
 
   /**
@@ -186,9 +186,11 @@ class UrlTile extends TileSource {
   setUrls(urls) {
     this.urls = urls;
     const key = urls.join('\n');
-    this.setTileUrlFunction(this.fixedTileUrlFunction ?
-      this.fixedTileUrlFunction.bind(this) :
-      createFromTemplates(urls, this.tileGrid), key);
+    if (this.generateTileUrlFunction_) {
+      this.setTileUrlFunction(createFromTemplates(urls, this.tileGrid), key);
+    } else {
+      this.setKey(key);
+    }
   }
 
   /**
@@ -203,10 +205,4 @@ class UrlTile extends TileSource {
 }
 
 
-/**
- * @type {import("../Tile.js").UrlFunction|undefined}
- * @protected
- */
-UrlTile.prototype.fixedTileUrlFunction;
-
 export default UrlTile;
diff --git a/src/ol/source/WMTS.js b/src/ol/source/WMTS.js
index ae957552e3..ef7615b708 100644
--- a/src/ol/source/WMTS.js
+++ b/src/ol/source/WMTS.js
@@ -159,9 +159,7 @@ class WMTS extends TileImage {
   setUrls(urls) {
     this.urls = urls;
     const key = urls.join('\n');
-    this.setTileUrlFunction(this.fixedTileUrlFunction ?
-      this.fixedTileUrlFunction.bind(this) :
-      createFromTileUrlFunctions(urls.map(createFromWMTSTemplate.bind(this))), key);
+    this.setTileUrlFunction(createFromTileUrlFunctions(urls.map(createFromWMTSTemplate.bind(this))), key);
   }
 
   /**
diff --git a/test/spec/ol/source/tilewms.test.js b/test/spec/ol/source/tilewms.test.js
index a00fd9e67b..8a7563d17e 100644
--- a/test/spec/ol/source/tilewms.test.js
+++ b/test/spec/ol/source/tilewms.test.js
@@ -310,7 +310,7 @@ describe('ol.source.TileWMS', function() {
   });
 
   describe('#setUrls()', function() {
-    it ('updates the source key', function() {
+    it('updates the source key', function() {
       const source = new TileWMS({
         urls: ['u1', 'u2']
       });