diff --git a/holoviews/streams.py b/holoviews/streams.py
index 0b439cc1d1..a3444d01e5 100644
--- a/holoviews/streams.py
+++ b/holoviews/streams.py
@@ -166,30 +166,42 @@ def trigger(cls, streams):
     def _on_trigger(self):
         """Called when a stream has been triggered"""
 
+
     @classmethod
     def _process_streams(cls, streams):
         """
         Processes a list of streams promoting Parameterized objects and
         methods to Param based streams.
         """
-        param_watch_support = util.param_version >= '1.8.0'
-        parameterizeds = [s.parameterized for s in streams if isinstance(s, Params)]
+        parameterizeds = defaultdict(set)
         valid, invalid = [], []
         for s in streams:
-            if not isinstance(s, Stream):
-                if isinstance(s, param.Parameterized) and param_watch_support:
-                    if s not in parameterizeds:
-                        s = Params(s)
-                    else:
-                        continue
-                elif util.is_param_method(s) and param_watch_support:
-                    if not hasattr(s, "_dinfo") or util.get_method_owner(s) in parameterizeds:
-                        continue
-                    else:
-                        s = ParamMethod(s)
-                else:
-                    invalid.append(s)
+            if isinstance(s, Stream):
+                pass
+            elif isinstance(s, param.Parameter):
+                s = Params(s.owner, [s.name])
+            elif isinstance(s, param.Parameterized):
+                s = Params(s)
+            elif util.is_param_method(s):
+                if not hasattr(s, "_dinfo"):
                     continue
+                s = ParamMethod(s)
+            else:
+                invalid.append(s)
+                continue
+            if isinstance(s, Params):
+                pid = id(s.parameterized)
+                overlap = (set(s.parameters) & parameterizeds[pid])
+                if overlap:
+                    pname = type(s.parameterized).__name__
+                    param.main.param.warning(
+                        'The %s parameter(s) on the %s object have '
+                        'already been supplied in another stream. '
+                        'Ensure that the supplied streams only specify '
+                        'each parameter once, otherwise multiple '
+                        'events will be triggered when the parameter '
+                        'changes.' % (sorted(overlap), pname))
+                parameterizeds[pid] |= set(s.parameters)
             valid.append(s)
         return valid, invalid
 
diff --git a/holoviews/tests/teststreams.py b/holoviews/tests/teststreams.py
index f0c2dd1869..0476b615d6 100644
--- a/holoviews/tests/teststreams.py
+++ b/holoviews/tests/teststreams.py
@@ -12,6 +12,9 @@
 from holoviews.streams import * # noqa (Test all available streams)
 from holoviews.util import Dynamic
 
+from .utils import LoggingComparisonTestCase
+
+
 def test_all_stream_parameters_constant():
     all_stream_cls = [v for v in globals().values() if
                       isinstance(v, type) and issubclass(v, Stream)]
@@ -178,12 +181,9 @@ def test_class_value_update(self):
 
 
 
-class TestParamsStream(ComparisonTestCase):
+class TestParamsStream(LoggingComparisonTestCase):
 
     def setUp(self):
-        if LooseVersion(param.__version__) < '1.8.0':
-            raise SkipTest('Params stream requires param >= 1.8.0')
-
         class Inner(param.Parameterized):
 
             x = param.Number(default = 0)
@@ -223,6 +223,41 @@ def subscriber(**kwargs):
         inner.y = 2
         self.assertEqual(values, [{'x': 2, 'y': 2}])
 
+    def test_param_stream_instance_separate_parameters(self):
+        inner = self.inner()
+
+        xparam = Params(inner, ['x'])
+        yparam = Params(inner, ['y'])
+
+        valid, invalid = Stream._process_streams([xparam, yparam])
+        self.assertEqual(len(valid), 2)
+        self.assertEqual(len(invalid), 0)
+
+    def test_param_stream_instance_overlapping_parameters(self):
+        inner = self.inner()
+
+        params1 = Params(inner)
+        params2 = Params(inner)
+
+        Stream._process_streams([params1, params2])
+        self.log_handler.assertContains('WARNING', "['x', 'y']")
+
+    def test_param_parameter_instance_separate_parameters(self):
+        inner = self.inner()
+
+        valid, invalid = Stream._process_streams([inner.param.x, inner.param.y])
+        xparam, yparam = valid
+
+        self.assertIs(xparam.parameterized, inner)
+        self.assertEqual(xparam.parameters, ['x'])
+        self.assertIs(yparam.parameterized, inner)
+        self.assertEqual(yparam.parameters, ['y'])
+
+    def test_param_parameter_instance_overlapping_parameters(self):
+        inner = self.inner()
+        Stream._process_streams([inner.param.x, inner.param.x])
+        self.log_handler.assertContains('WARNING', "['x']")
+
     def test_param_stream_parameter_override(self):
         inner = self.inner(x=2)
         stream = Params(inner, parameters=['x'])