diff --git a/holoviews/plotting/bokeh/plot.py b/holoviews/plotting/bokeh/plot.py
index 91a72967b6..109b7067e3 100644
--- a/holoviews/plotting/bokeh/plot.py
+++ b/holoviews/plotting/bokeh/plot.py
@@ -249,10 +249,12 @@ def cleanup(self):
             if plot.subplots:
                 plot.subplots.clear()
 
-            if isinstance(plot, GenericElementPlot):
-                for callback in plot.callbacks:
-                    streams += callback.streams
-                    callback.cleanup()
+            if not isinstance(plot, (GenericElementPlot, GenericOverlayPlot)):
+                continue
+
+            for callback in plot.callbacks:
+                streams += callback.streams
+                callback.cleanup()
 
             for stream in set(streams):
                 stream._subscribers = [
@@ -261,7 +263,6 @@ def cleanup(self):
                     get_method_owner(subscriber) not in plots
                 ]
 
-
     def _fontsize(self, key, label='fontsize', common=True):
         """
         Converts integer fontsizes to a string specifying
diff --git a/holoviews/plotting/plot.py b/holoviews/plotting/plot.py
index eb963afea2..444dd68120 100644
--- a/holoviews/plotting/plot.py
+++ b/holoviews/plotting/plot.py
@@ -195,7 +195,7 @@ def cleanup(self):
         """
         plots = self.traverse(lambda x: x, [Plot])
         for plot in plots:
-            if not isinstance(plot, (GenericCompositePlot, GenericElementPlot, GenericOverlayPlot)):
+            if not isinstance(plot, (GenericElementPlot, GenericOverlayPlot)):
                 continue
             for stream in set(plot.streams):
                 stream._subscribers = [
diff --git a/holoviews/tests/plotting/bokeh/test_plot.py b/holoviews/tests/plotting/bokeh/test_plot.py
index 5c7a08a2e1..03c9761f27 100644
--- a/holoviews/tests/plotting/bokeh/test_plot.py
+++ b/holoviews/tests/plotting/bokeh/test_plot.py
@@ -14,9 +14,11 @@
 from holoviews import Curve
 from holoviews.core.element import Element
 from holoviews.core.options import Store
+from holoviews.core.spaces import DynamicMap
 from holoviews.element.comparison import ComparisonTestCase
 from holoviews.plotting.bokeh.callbacks import Callback
 from holoviews.plotting.bokeh.element import ElementPlot
+from holoviews.streams import Pipe
 
 bokeh_renderer = Store.renderers['bokeh']
 
@@ -82,11 +84,60 @@ def _test_hover_info(self, element, tooltips, line_policy='nearest', formatters=
                     self.assertIn(lookup[2:-1], cds.data)
 
         # Ensure all the glyph renderers have a hover tool
-        print(renderers, hover)
         for renderer in renderers:
             self.assertTrue(any(renderer in h.renderers for h in hover))
 
 
+def test_element_plot_stream_cleanup():
+    stream = Pipe()
+
+    dmap = DynamicMap(Curve, streams=[stream])
+
+    plot = bokeh_renderer.get_plot(dmap)
+
+    assert len(stream._subscribers) == 1
+
+    plot.cleanup()
+
+    assert not stream._subscribers
+
+
+def test_overlay_plot_stream_cleanup():
+    stream1 = Pipe()
+    stream2 = Pipe()
+
+    dmap1 = DynamicMap(Curve, streams=[stream1])
+    dmap2 = DynamicMap(Curve, streams=[stream2])
+
+    plot = bokeh_renderer.get_plot(dmap1 * dmap2)
+
+    assert len(stream1._subscribers) == 4
+    assert len(stream2._subscribers) == 4
+
+    plot.cleanup()
+
+    assert not stream1._subscribers
+    assert not stream2._subscribers
+
+
+def test_layout_plot_stream_cleanup():
+    stream1 = Pipe()
+    stream2 = Pipe()
+
+    dmap1 = DynamicMap(Curve, streams=[stream1])
+    dmap2 = DynamicMap(Curve, streams=[stream2])
+
+    plot = bokeh_renderer.get_plot(dmap1 + dmap2)
+
+    assert len(stream1._subscribers) == 2
+    assert len(stream2._subscribers) == 2
+
+    plot.cleanup()
+
+    assert not stream1._subscribers
+    assert not stream2._subscribers
+
+
 def test_sync_two_plots():
     curve = lambda i: Curve(np.arange(10) * i, label="ABC"[i])
     plot1 = curve(0) * curve(1)
diff --git a/holoviews/tests/plotting/plotly/test_plot.py b/holoviews/tests/plotting/plotly/test_plot.py
index 3a033f8848..0f71a99521 100644
--- a/holoviews/tests/plotting/plotly/test_plot.py
+++ b/holoviews/tests/plotting/plotly/test_plot.py
@@ -2,16 +2,68 @@
 import pyviz_comms as comms
 from param import concrete_descendents
 
-from holoviews.core import Store
+from holoviews.core import DynamicMap, Store
+from holoviews.element import Curve
 from holoviews.element.comparison import ComparisonTestCase
 from holoviews.plotting.plotly.element import ElementPlot
 from holoviews.plotting.plotly.util import figure_grid
+from holoviews.streams import Pipe
 
 from .. import option_intersections
 
 plotly_renderer = Store.renderers['plotly']
 
 
+def test_element_plot_stream_cleanup():
+    stream = Pipe()
+
+    dmap = DynamicMap(Curve, streams=[stream])
+
+    plot = plotly_renderer.get_plot(dmap)
+
+    assert len(stream._subscribers) == 1
+
+    plot.cleanup()
+
+    assert not stream._subscribers
+
+
+def test_overlay_plot_stream_cleanup():
+    stream1 = Pipe()
+    stream2 = Pipe()
+
+    dmap1 = DynamicMap(Curve, streams=[stream1])
+    dmap2 = DynamicMap(Curve, streams=[stream2])
+
+    plot = plotly_renderer.get_plot(dmap1 * dmap2)
+
+    assert len(stream1._subscribers) == 4
+    assert len(stream2._subscribers) == 4
+
+    plot.cleanup()
+
+    assert not stream1._subscribers
+    assert not stream2._subscribers
+
+
+def test_layout_plot_stream_cleanup():
+    stream1 = Pipe()
+    stream2 = Pipe()
+
+    dmap1 = DynamicMap(Curve, streams=[stream1])
+    dmap2 = DynamicMap(Curve, streams=[stream2])
+
+    plot = plotly_renderer.get_plot(dmap1 + dmap2)
+
+    assert len(stream1._subscribers) == 2
+    assert len(stream2._subscribers) == 2
+
+    plot.cleanup()
+
+    assert not stream1._subscribers
+    assert not stream2._subscribers
+
+
 class TestPlotlyPlot(ComparisonTestCase):
 
     def setUp(self):