diff --git a/doc/Tutorials/Dynamic_Map.ipynb b/doc/Tutorials/Dynamic_Map.ipynb
index 9f5fe5a168..0b870cf978 100644
--- a/doc/Tutorials/Dynamic_Map.ipynb
+++ b/doc/Tutorials/Dynamic_Map.ipynb
@@ -250,7 +250,56 @@
     "\n",
     "* There must be as many positional arguments in the callable signature as key dimensions.\n",
     "* The argument order in the callable signature must match the order of the declared key dimensions.\n",
-    "* All key dimensions are defined with a bounded ``range`` or ``values`` parameter (for categorical dimensions)."
+    "* All key dimensions are defined with a bounded ``range`` or ``values`` parameter (for categorical dimensions).\n",
+    "\n",
+    "Here is another example of a bounded ``DynamicMap``:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def shapes(N, radius=0.5): # Positional keyword arguments are fine\n",
+    "    paths = [hv.Path([[(radius*np.sin(a), radius*np.cos(a)) \n",
+    "                        for a in np.linspace(-np.pi, np.pi, n+2)]], \n",
+    "                     extents=(-1,-1,1,1)) \n",
+    "             for n in range(N,N+3)]\n",
+    "    return hv.Overlay(paths)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "%%opts Path (linewidth=1.5)\n",
+    "dmap = hv.DynamicMap(shapes, kdims=[hv.Dimension('N', range=(2,20)), hv.Dimension('radius', range=(0.5,1))])\n",
+    "dmap"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As you can see, you can return ``Overlays`` from ``DynamicMaps`` and ``DynamicMaps`` can be styled in exactly the same way as ``HoloMaps``. Note that currently, ``Overlay`` objects should be returned from the callable and the ``*`` operator is not yet supported at the ``DynamicMap`` level. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%opts Path (linewidth=1.5)"
    ]
   },
   {
@@ -321,7 +370,7 @@
    },
    "outputs": [],
    "source": [
-    "dmap[{(0,0.01), (0,0.5), (0.5,0.01), (0.5,0.5)}] # Returns a *new* DynamicMap with the sampled keys in it's cache"
+    "dmap[{(2,0.5), (2,1.0), (3,0.5), (3,1.0)}] # Returns a *new* DynamicMap with the specified keys in it's cache"
    ]
   },
   {
@@ -343,7 +392,7 @@
    },
    "outputs": [],
    "source": [
-    "dmap[{0,0.5},{0.01,0.5}]"
+    "dmap[{2,3},{0.5,1.0}]"
    ]
   },
   {
@@ -404,7 +453,7 @@
    },
    "outputs": [],
    "source": [
-    "sliced = dmap[0.2:0.8, :]\n",
+    "sliced = dmap[4:8, :]\n",
     "sliced"
    ]
   },
@@ -423,7 +472,7 @@
    },
    "outputs": [],
    "source": [
-    "sliced[:, 0.05:0.1]"
+    "sliced[:, 0.8:1.0]"
    ]
   },
   {
@@ -471,8 +520,8 @@
    },
    "outputs": [],
    "source": [
-    "hv.DynamicMap(sine_image, kdims=[hv.Dimension('phase',values=[0,0.5]),\n",
-    "                                 hv.Dimension('frequency',  values=[0.01,0.5])])"
+    "hv.DynamicMap(shapes, kdims=[hv.Dimension('N', values=[2,3,4,5]), \n",
+    "                             hv.Dimension('radius', values=[0.7,0.8,0.9,1])])\n"
    ]
   },
   {
@@ -497,7 +546,7 @@
    },
    "outputs": [],
    "source": [
-    "dmap = hv.DynamicMap(sine_image, kdims=['phase', 'frequency'], sampled=True)\n",
+    "dmap = hv.DynamicMap(shapes, kdims=['N', 'radius'], sampled=True)\n",
     "dmap"
    ]
   },
@@ -516,7 +565,7 @@
    },
    "outputs": [],
    "source": [
-    "dmap[{0,0.5},{0.01,0.5}]"
+    "dmap[{2,3},{0.5,1.0}]"
    ]
   },
   {
@@ -534,9 +583,8 @@
    },
    "outputs": [],
    "source": [
-    "dmap + hv.HoloMap({(p,f):sine_image(p, f) \n",
-    "                   for p in [0,0.5,1,1.5] \n",
-    "                   for f in [0.5,0.75]}, kdims=['phase', 'frequency'])"
+    "(dmap + hv.HoloMap({(N,r):shapes(N, r) for N in [3,4,5] \n",
+    "                    for r in [0.5,0.75]}, kdims=['N', 'radius']))"
    ]
   },
   {