diff --git a/docs/config.rst b/docs/config.rst
index 97d4db9..9eb188b 100644
--- a/docs/config.rst
+++ b/docs/config.rst
@@ -24,8 +24,9 @@ attributes:
         are iterated in ascending creation order (consistent with
         ``dict`` in Python 3.7+); otherwise in ascending alphanumeric
         order.  Global configuration value can be overridden for
-        particular file and its subgroups by specifying ``track_order`` argument to
-        :class:`h5py.File`. The default is ``False``.
+        particular container by specifying ``track_order`` argument to
+        :class:`h5py.File`, :meth:`h5py.Group.create_group`,
+        :meth:`h5py.Group.create_dataset`.  The default is ``False``.
 
 
 IPython
diff --git a/test/hl/test_attribute.py b/test/hl/test_attribute.py
index a0388fe..c6fc5ee 100644
--- a/test/hl/test_attribute.py
+++ b/test/hl/test_attribute.py
@@ -118,6 +118,68 @@ def test_create(self):
         # close file
         f.close()
 
+    def test_attribute_alphanumeric_order(self):
+        filename = self.getFileName("attribute_order")
+
+        # disable track_order
+        f = h5py.File(filename, 'w', track_order=False)
+
+        # Attributes on a group should be iterated through in alphanumeric order
+        g1 = f.create_group('g1')
+
+        g1.attrs['Z'] = 0
+        g1.attrs['Y'] = 1
+        g1.attrs.create('W', 2)
+        g1.attrs['X'] = 3
+        g1.attrs['V'] = 4
+
+        expected_sequence = ['V', 'W', 'X', 'Y', 'Z']
+
+        for i, attr in enumerate(g1.attrs):
+            self.assertEqual(attr, expected_sequence[i])
+
+        # Attributes on a dataset should be iterated through in alphanumeric order
+        dset = g1.create_dataset('dset', data=[1, 2, 3])
+        dset.attrs['Z'] = 0
+        dset.attrs['Y'] = 1
+        dset.attrs.create('W', 2)
+        dset.attrs['X'] = 3
+        dset.attrs['V'] = 4
+
+        for i, attr in enumerate(dset.attrs):
+            self.assertEqual(attr, expected_sequence[i])
+
+    def test_attribute_creation_order(self):
+        filename = self.getFileName("attribute_order")
+
+        # enable track_order
+        f = h5py.File(filename, 'w', track_order=True)
+
+        # Attributes on a group should be iterated through in creation order
+        g1 = f.create_group('g1')
+
+        g1.attrs['Z'] = 0
+        g1.attrs['Y'] = 1
+        g1.attrs.create('W', 2)
+        g1.attrs['X'] = 3
+        g1.attrs['V'] = 4
+
+        expected_sequence = ['Z', 'Y', 'W', 'X', 'V']
+
+        for i, attr in enumerate(g1.attrs):
+            self.assertEqual(attr, expected_sequence[i])
+
+        # Attributes on a dataset should be iterated through in creation order
+        dset = g1.create_dataset('dset', data=[1, 2, 3])
+        dset.attrs['Z'] = 0
+        dset.attrs['Y'] = 1
+        dset.attrs.create('W', 2)
+        dset.attrs['X'] = 3
+        dset.attrs['V'] = 4
+
+        for i, attr in enumerate(dset.attrs):
+            self.assertEqual(attr, expected_sequence[i])
+
 
 if __name__ == '__main__':
     loglevel = logging.ERROR
diff --git a/test/hl/test_file.py b/test/hl/test_file.py
index c76d915..0bceaee 100644
--- a/test/hl/test_file.py
+++ b/test/hl/test_file.py
@@ -348,13 +348,39 @@ def test_close(self):
         f.close()
         self.assertFalse(f)
 
+    def test_link_alphanumeric_order(self):
+        filename = self.getFileName("alphanumeric_order")
+        # default order of links is alphanumeric
+        f = h5py.File(filename, 'w', track_order=False)
+
+        f.create_dataset('dset', data=[1, 2, 3])
+
+        f['A'] = h5py.SoftLink('/group')
+        f['C'] = h5py.SoftLink('/dset')
+        f['B'] = f['dset']
+
+        expected_sequence = ["A", "B", "C", "dset"]
+
+        for i, item in enumerate(f):
+            self.assertEqual(item, expected_sequence[i])
+
+        # test for links within a subgroup
+        g = f.create_group('group')
+        g['Z'] = h5py.SoftLink('/dset')
+        g['X'] = h5py.SoftLink('/group')
+        g['Y'] = f['dset']
+
+        expected_sequence = ["X", "Y", "Z"]
+
+        for i, item in enumerate(g):
+            self.assertEqual(item, expected_sequence[i])
+
     def test_link_creation_order(self):
         filename = self.getFileName("track_order")
         f = h5py.File(filename, 'w', track_order=True)
 
         f.create_dataset('dset', data=[1, 2, 3])
 
-        # create links in group g2
         f['A'] = h5py.SoftLink('/group')
         f['C'] = h5py.SoftLink('/dset')
         f['B'] = f['dset']