diff --git a/cloudpickle/cloudpickle_fast.py b/cloudpickle/cloudpickle_fast.py
index 46a9540ec..e14e4710d 100644
--- a/cloudpickle/cloudpickle_fast.py
+++ b/cloudpickle/cloudpickle_fast.py
@@ -155,8 +155,8 @@ def _function_getstate(func):
     }
 
     f_globals_ref = _extract_code_globals(func.__code__)
-    f_globals = {k: func.__globals__[k] for k in f_globals_ref if k in
-                 func.__globals__}
+    f_globals = {k: func.__globals__[k] for k in sorted(f_globals_ref)
+                 if k in func.__globals__}
 
     closure_values = (
         list(map(_get_cell_contents, func.__closure__))
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 845f27962..7784f5769 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -24,6 +24,7 @@
 import enum
 import typing
 from functools import wraps
+import time
 
 import pytest
 
@@ -49,6 +50,7 @@
 from cloudpickle.cloudpickle import _extract_class_dict, _whichmodule
 from cloudpickle.cloudpickle import _lookup_module_and_qualname
 
+from .testutils import subprocess_pickle_string
 from .testutils import subprocess_pickle_echo
 from .testutils import assert_run_python_script
 from .testutils import subprocess_worker
@@ -57,6 +59,9 @@
 
 
 _TEST_GLOBAL_VARIABLE = "default_value"
+_TEST_GLOBAL_VARIABLE2 = "another_value"
+
+exec("def _TEST_BIG_GLOBAL_SPACE():\n    return %s" % ", ".join([f"a{i}" for i in range(1000)]))
 
 
 class RaiserOnPickle(object):
@@ -2321,6 +2326,32 @@ def __type__(self):
         o = MyClass()
         pickle_depickle(o, protocol=self.protocol)
 
+    @pytest.mark.skipif(
+        sys.version_info < (3, 6, 0),
+        reason="Dict determinism is a lost cause in Python < 3.6")
+    def test_sorted_globals(self):
+        vals = set()
+
+        def func_with_globals():
+            return _TEST_GLOBAL_VARIABLE + _TEST_GLOBAL_VARIABLE2
+
+        for i in range(5):
+            vals.add(
+                subprocess_pickle_string(func_with_globals,
+                                         protocol=self.protocol,
+                                         add_env={"PYTHONHASHSEED": str(i)}))
+        assert len(vals) == 1
+
+    def test_efficient_sorted_globals(self):
+        # Non regression test to demonstrate that large numbers of globals
+        # do not cause slowdown
+        gvars = set(f"a{i}" for i in range(1000))
+        assert cloudpickle.cloudpickle._extract_code_globals(
+            _TEST_BIG_GLOBAL_SPACE.__code__) == gvars
+        tic = time.time()
+        subprocess_pickle_string(_TEST_BIG_GLOBAL_SPACE, protocol=self.protocol)
+        assert time.time() - tic < 0.5
+
 
 class Protocol2CloudPickleTest(CloudPickleTest):
 
diff --git a/tests/testutils.py b/tests/testutils.py
index 6acc998d4..9c7d5c47d 100644
--- a/tests/testutils.py
+++ b/tests/testutils.py
@@ -38,24 +38,25 @@ def _make_cwd_env():
     return cloudpickle_repo_folder, env
 
 
-def subprocess_pickle_echo(input_data, protocol=None, timeout=TIMEOUT):
-    """Echo function with a child Python process
+def subprocess_pickle_string(input_data, protocol=None, timeout=TIMEOUT,
+                             add_env=None):
+    """Retrieve pickle string of an object generated by a child Python process
 
     Pickle the input data into a buffer, send it to a subprocess via
     stdin, expect the subprocess to unpickle, re-pickle that data back
-    and send it back to the parent process via stdout for final unpickling.
+    and send it back to the parent process via stdout.
 
-    >>> subprocess_pickle_echo([1, 'a', None])
-    [1, 'a', None]
+    >>> testutils.subprocess_pickle_string([1, 'a', None], protocol=2)
+    b'\x80\x02]q\x00(K\x01X\x01\x00\x00\x00aq\x01Ne.'
 
     """
-    # run then pickle_echo(protocol=protocol) in __main__:
-
     # Protect stderr from any warning, as we will assume an error will happen
     # if it is not empty. A concrete example is pytest using the imp module,
     # which is deprecated in python 3.8
     cmd = [sys.executable, '-W ignore', __file__, "--protocol", str(protocol)]
     cwd, env = _make_cwd_env()
+    if add_env:
+        env.update(add_env)
     proc = Popen(cmd, stdin=PIPE, stdout=PIPE, stderr=PIPE, cwd=cwd, env=env,
                  bufsize=4096)
     pickle_string = dumps(input_data, protocol=protocol)
@@ -67,7 +68,7 @@ def subprocess_pickle_echo(input_data, protocol=None, timeout=TIMEOUT):
             message = "Subprocess returned %d: " % proc.returncode
             message += err.decode('utf-8')
             raise RuntimeError(message)
-        return loads(out)
+        return out
     except TimeoutExpired as e:
         proc.kill()
         out, err = proc.communicate()
@@ -75,6 +76,25 @@ def subprocess_pickle_echo(input_data, protocol=None, timeout=TIMEOUT):
         raise RuntimeError(message) from e
 
 
+def subprocess_pickle_echo(input_data, protocol=None, timeout=TIMEOUT,
+                           add_env=None):
+    """Echo function with a child Python process
+
+    Pickle the input data into a buffer, send it to a subprocess via
+    stdin, expect the subprocess to unpickle, re-pickle that data back
+    and send it back to the parent process via stdout for final unpickling.
+
+    >>> subprocess_pickle_echo([1, 'a', None])
+    [1, 'a', None]
+
+    """
+    out = subprocess_pickle_string(input_data,
+                                   protocol=protocol,
+                                   timeout=timeout,
+                                   add_env=add_env)
+    return loads(out)
+
+
 def _read_all_bytes(stream_in, chunk_size=4096):
     all_data = b""
     while True: