diff --git a/param/parameterized.py b/param/parameterized.py
index 17e4a6dd..2f88df94 100644
--- a/param/parameterized.py
+++ b/param/parameterized.py
@@ -2104,7 +2104,7 @@ def _instantiate_param(self_, param_obj, dict_=None, key=None, deepcopy=True):
 
         dict_[key] = new_object
 
-        if isinstance(new_object, Parameterized):
+        if isinstance(new_object, Parameterized) and deepcopy:
             global object_count
             object_count += 1
             # Writes over name given to the original object;
diff --git a/tests/testparameterizedobject.py b/tests/testparameterizedobject.py
index ffc56fd8..f9b5ea76 100644
--- a/tests/testparameterizedobject.py
+++ b/tests/testparameterizedobject.py
@@ -833,6 +833,26 @@ def test_update_context_multi_parameter(self):
         assert t.inst == 'foo'
         assert t.notinst == 1
 
+    def test_constant_readonly_parameterized(self):
+        class ParamClass(param.Parameterized):
+            x = param.Number()
+
+        pc1 = ParamClass(name="FOO1")
+        pc2 = ParamClass(name="FOO2")
+
+        class P(param.Parameterized):
+            ro = param.Parameter(pc1, constant=True)
+            const = param.Parameter(pc2, readonly=True)
+            ro_i = param.Parameter(pc1, constant=True, instantiate=True)
+            const_i = param.Parameter(pc2, readonly=True, instantiate=True)
+
+        p = P()
+
+        assert p.ro.name == 'FOO1'
+        assert p.const.name == 'FOO2'
+        assert p.ro_i.name.startswith('ParamClass0')
+        assert p.const_i.name == 'FOO2'
+
 
 class some_fn(param.ParameterizedFunction):
     __test__ = False