diff --git a/holoviews/core/spaces.py b/holoviews/core/spaces.py
index 3168cba410..275a25561e 100644
--- a/holoviews/core/spaces.py
+++ b/holoviews/core/spaces.py
@@ -446,6 +446,19 @@ def __init__(self, callable, **params):
     def argspec(self):
         return util.argspec(self.callable)
 
+
+    def clone(self, callable=None, **overrides):
+        """
+        Allows making a copy of the Callable optionally overriding
+        the callable and other parameters.
+        """
+        old = {k: v for k, v in self.get_param_values()
+               if k not in ['callable', 'name']}
+        params = dict(old, **overrides)
+        callable = self.callable if callable is None else callable
+        return self.__class__(callable, **params)
+
+
     def __call__(self, *args, **kwargs):
         inputs = [i for i in self.inputs if isinstance(i, DynamicMap)]
         streams = []
@@ -667,9 +680,19 @@ def clone(self, data=None, shared_data=True, new_type=None, *args, **overrides):
         """
         if data is None and shared_data:
             data = self.data
-        return super(UniformNdMapping, self).clone(overrides.pop('callback', self.callback),
-                                                   shared_data, new_type,
-                                                   *(data,) + args, **overrides)
+        clone = super(UniformNdMapping, self).clone(overrides.pop('callback', self.callback),
+                                                    shared_data, new_type,
+                                                    *(data,) + args, **overrides)
+
+        # Ensure the clone references this object to ensure
+        # stream sources are inherited
+        if clone.callback is self.callback:
+            clone.callback = self.callback.clone()
+        if self not in clone.callback.inputs:
+            with util.disable_constant(clone.callback):
+                clone.callback.inputs = clone.callback.inputs+[self]
+        return clone
+
 
     def reset(self):
         """
@@ -1096,13 +1119,7 @@ def reindex(self, kdims=[], force=False):
         if dropped:
             raise ValueError("DynamicMap does not allow dropping dimensions, "
                              "reindex may only be used to reorder dimensions.")
-        reindexed = super(DynamicMap, self).reindex(kdims, force)
-        def reindex(*args, **kwargs):
-            keymap = {kd.name: arg for kd, arg in zip(self.kdims, args)}
-            keymap.update(kwargs)
-            args = tuple(keymap[kd.name] for kd in kdims)
-            return reindexed[args]
-        return reindexed.clone(callback=Callable(reindex, inputs=[self]))
+        return super(DynamicMap, self).reindex(kdims, force)
 
 
     def drop_dimension(self, dimensions):
diff --git a/holoviews/core/util.py b/holoviews/core/util.py
index 19055216e4..1ec9ad3ce1 100644
--- a/holoviews/core/util.py
+++ b/holoviews/core/util.py
@@ -7,6 +7,7 @@
 import datetime as dt
 from collections import defaultdict, Counter
 from functools import partial
+from contextlib import contextmanager
 
 import numpy as np
 import param
@@ -982,6 +983,25 @@ def get_param_values(data):
     return params
 
 
+@contextmanager
+def disable_constant(parameterized):
+    """
+    Temporarily set parameters on Parameterized object to
+    constant=False.
+    """
+    params = parameterized.params().values()
+    constants = [p.constant for p in params]
+    for param in params:
+        param.constant = False
+    try:
+        yield
+    except:
+        raise
+    finally:
+        for (param, const) in zip(params, constants):
+            param.constant = const
+
+
 def get_ndmapping_label(ndmapping, attr):
     """
     Function to get the first non-auxiliary object
diff --git a/holoviews/streams.py b/holoviews/streams.py
index 95423badba..c99a6734ce 100644
--- a/holoviews/streams.py
+++ b/holoviews/streams.py
@@ -32,25 +32,6 @@ def triggering_streams(streams):
             stream._triggering = False
 
 
-@contextmanager
-def disable_constant(parameterized):
-    """
-    Temporarily set parameters on Parameterized object to
-    constant=False.
-    """
-    params = parameterized.params().values()
-    constants = [p.constant for p in params]
-    for param in params:
-        param.constant = False
-    try:
-        yield
-    except:
-        raise
-    finally:
-        for (param, const) in zip(params, constants):
-            param.constant = const
-
-
 class Stream(param.Parameterized):
     """
     A Stream is simply a parameterized object with parameters that
@@ -118,7 +99,7 @@ def trigger(cls, streams):
                 subscriber(**dict(union))
 
         for stream in streams:
-            with disable_constant(stream):
+            with util.disable_constant(stream):
                 if stream.transient:
                     stream.reset()
 
@@ -175,7 +156,7 @@ def reset(self):
         """
         Resets stream parameters to their defaults.
         """
-        with disable_constant(self):
+        with util.disable_constant(self):
             for k, p in self.params().items():
                 if k != 'name':
                     setattr(self, k, p.default)
@@ -250,7 +231,7 @@ def _set_stream_parameters(self, **kwargs):
         Sets the stream parameters which are expected to be declared
         constant.
         """
-        with disable_constant(self) as constant:
+        with util.disable_constant(self) as constant:
             self.set_param(**kwargs)