diff --git a/pyomo/core/tests/unit/test_initializer.py b/pyomo/core/tests/unit/test_initializer.py
index 5767406bdf7..b334a6b857b 100644
--- a/pyomo/core/tests/unit/test_initializer.py
+++ b/pyomo/core/tests/unit/test_initializer.py
@@ -11,6 +11,8 @@
 
 import functools
 import pickle
+import platform
+import sys
 import types
 
 import pyomo.common.unittest as unittest
@@ -37,6 +39,9 @@
 from pyomo.environ import ConcreteModel, Var
 
 
+is_pypy = platform.python_implementation().lower().startswith("pypy")
+
+
 def _init_scalar(m):
     return 1
 
@@ -561,12 +566,20 @@ def test_no_argspec(self):
         self.assertFalse(a.contains_indices())
         self.assertEqual(a('111', 2), 7)
 
-        # Special case: getfullargspec fails on int, so we assume it is
-        # always an IndexedCallInitializer
+        # Special case: getfullargspec fails for int under CPython and
+        # PyPy<7.3.14, so we assume it is an IndexedCallInitializer.
         basetwo = functools.partial(int, '101', base=2)
         a = Initializer(basetwo)
-        self.assertIs(type(a), IndexedCallInitializer)
-        self.assertFalse(a.constant())
+        if is_pypy and sys.pypy_version_info[:3] >= (7, 3, 14):
+            # PyPy behavior diverged from CPython in 7.3.14.  Arguably
+            # this is "more correct", so we will allow the difference to
+            # persist through Pyomo's Initializer handling (and not
+            # special case it there)
+            self.assertIs(type(a), ScalarCallInitializer)
+            self.assertTrue(a.constant())
+        else:
+            self.assertIs(type(a), IndexedCallInitializer)
+            self.assertFalse(a.constant())
         self.assertFalse(a.verified)
         self.assertFalse(a.contains_indices())
         # but this is not callable, as int won't accept the 'model'
diff --git a/pyomo/core/tests/unit/test_pickle.py b/pyomo/core/tests/unit/test_pickle.py
index 808db2e45f3..861704a2f9c 100644
--- a/pyomo/core/tests/unit/test_pickle.py
+++ b/pyomo/core/tests/unit/test_pickle.py
@@ -35,7 +35,7 @@
 )
 
 
-using_pypy = platform.python_implementation() == "PyPy"
+is_pypy = platform.python_implementation().lower().startswith("pypy")
 
 
 def obj_rule(model):
@@ -322,7 +322,7 @@ def rule2(model, i):
         model.con = Constraint(rule=rule1)
         model.con2 = Constraint(model.a, rule=rule2)
         instance = model.create_instance()
-        if using_pypy:
+        if is_pypy:
             str_ = pickle.dumps(instance)
             tmp_ = pickle.loads(str_)
         else: