diff --git a/dill/_dill.py b/dill/_dill.py
index be0aeba2..2aae255e 100644
--- a/dill/_dill.py
+++ b/dill/_dill.py
@@ -60,7 +60,7 @@
 # import zlib
 from weakref import ReferenceType, ProxyType, CallableProxyType
 from collections import OrderedDict
-from functools import partial
+from functools import lru_cache, partial
 from operator import itemgetter, attrgetter
 GENERATOR_FAIL = False
 import importlib.machinery
@@ -1028,6 +1028,23 @@ def _import_module(import_name, safe=False):
             return None
         raise
 
+@lru_cache(maxsize=2**3)
+def _import_module_copy(module_name, safe=False):
+    """load (a copy of) a module without adding it to sys.modules"""
+    import importlib.util
+    try:
+        spec = importlib.util.find_spec(module_name)
+        if spec is None:
+            raise ModuleNotFoundError("No module named %r" % module_name)
+        module = importlib.util.module_from_spec(spec)
+        spec.loader.exec_module(module)
+    except ImportError:
+        if safe:
+            return None
+        else:
+            raise
+    return module
+
 # https://github.com/python/cpython/blob/a8912a0f8d9eba6d502c37d522221f9933e976db/Lib/pickle.py#L322-L333
 def _getattribute(obj, name):
     for subpath in name.split('.'):
@@ -1047,23 +1064,24 @@ def _locate_function(obj, pickler=None):
     if module_name in ['__main__', None] or \
             pickler and is_dill(pickler, child=False) and pickler._session and module_name == pickler._main.__name__:
         return False
-    if hasattr(obj, '__qualname__'):
+    unloaded_module = module_name not in sys.modules
+    if unloaded_module:
+        module = _import_module_copy(module_name, safe=True)
+    else:
         module = _import_module(module_name, safe=True)
-        try:
-            found, _ = _getattribute(module, obj.__qualname__)
-            return found is obj
-        except AttributeError:
-            return False
+    try:
+        found, _ = _getattribute(module, getattr(obj, '__qualname__', obj.__name__))
+    except AttributeError:
+        return False
+    if unloaded_module and inspect.isfunction(obj) and obj.__code__ == found.__code__:
+        return found
     else:
-        found = _import_module(module_name + '.' + obj.__name__, safe=True)
         return found is obj
 
-
 def _setitems(dest, source):
     for k, v in source.items():
         dest[k] = v
 
-
 def _save_with_postproc(pickler, reduction, is_pickler_dill=None, obj=Getattr.NO_DEFAULT, postproc_list=None):
     if obj is Getattr.NO_DEFAULT:
         obj = Reduce(reduction) # pragma: no cover
@@ -1765,7 +1783,8 @@ def save_classmethod(pickler, obj):
 
 @register(FunctionType)
 def save_function(pickler, obj):
-    if not _locate_function(obj, pickler):
+    found_obj = _locate_function(obj, pickler)
+    if not found_obj:
         if type(obj.__code__) is not CodeType:
             # Some PyPy builtin functions have no module name, and thus are not
             # able to be located
@@ -1870,9 +1889,19 @@ def save_function(pickler, obj):
                     pickler.write(bytes('0', 'UTF-8'))
 
         logger.trace(pickler, "# F1")
+    elif type(found_obj) is not bool:
+        # Deal with global functions of unloaded modules.
+        logger.trace(pickler, "F3: %s", obj)
+        name = getattr(obj, '__qualname__', obj.__name__)
+        sys.modules[obj.__module__] = _import_module_copy(obj.__module__, safe=True) # cached
+        try:
+            StockPickler.save_global(pickler, found_obj, name=name)
+        finally:
+            del sys.modules[obj.__module__]
+        logger.trace(pickler, "F3: %s", obj)
     else:
         logger.trace(pickler, "F2: %s", obj)
-        name = getattr(obj, '__qualname__', getattr(obj, '__name__', None))
+        name = getattr(obj, '__qualname__', obj.__name__)
         StockPickler.save_global(pickler, obj, name=name)
         logger.trace(pickler, "# F2")
     return
diff --git a/dill/tests/test_functions.py b/dill/tests/test_functions.py
index d8c73396..e6c54c5d 100644
--- a/dill/tests/test_functions.py
+++ b/dill/tests/test_functions.py
@@ -132,7 +132,20 @@ def test_code_object():
         except Exception as error:
             raise Exception("failed to construct code object with format version {}".format(version)) from error
 
+def test_unloaded_module():
+    # Function should be saved as global until module is *re*loaded.
+    from statistics import mean
+    pickle_loaded = dill.dumps(mean)
+    del sys.modules['statistics']
+    pickle_unloaded = dill.dumps(mean)
+    assert 'statistics' not in sys.modules
+    import statistics
+    pickle_reloaded = dill.dumps(mean)
+    assert pickle_unloaded == pickle_loaded
+    assert pickle_reloaded != pickle_loaded
+
 if __name__ == '__main__':
     test_functions()
     test_issue_510()
     test_code_object()
+    test_unloaded_module()