tests/test_datatypes.py     |  7 ++++++-
 tests/test_elementpath.py   | 11 +++++++++--
 tests/test_schema_proxy.py  | 13 +++++++------
 tests/test_xpath2_parser.py |  1 -
 4 files changed, 22 insertions(+), 10 deletions(-)

diff --git a/tests/test_datatypes.py b/tests/test_datatypes.py
index 2dcafdf..01a9046 100644
--- a/tests/test_datatypes.py
+++ b/tests/test_datatypes.py
@@ -628,7 +628,12 @@ class TimezoneTypeTest(unittest.TestCase):
 
     def test_hashing(self):
         if sys.version_info < (3, 8):
-            self.assertEqual(hash(Timezone.fromstring('+05:00')), 1289844826723787395)
+            if sys.maxsize > 2**32:
+                self.assertEqual(
+                    hash(Timezone.fromstring('+05:00')), 1289844826723787395)
+            else:
+                self.assertEqual(
+                    hash(Timezone.fromstring('+05:00')), 943661699)
         else:
             self.assertEqual(hash(Timezone.fromstring('+05:00')), 7009945331308913293)
 
diff --git a/tests/test_elementpath.py b/tests/test_elementpath.py
index 6368b75..482d2f1 100644
--- a/tests/test_elementpath.py
+++ b/tests/test_elementpath.py
@@ -22,6 +22,11 @@
 #
 import unittest
 
+try:
+    import xmlschema
+except ImportError:
+    xmlschema = None
+
 if __name__ == '__main__':
     try:
         from tests.test_helpers import ExceptionHelpersTest, NamespaceHelpersTest, NodeHelpersTest
@@ -29,7 +34,8 @@ if __name__ == '__main__':
         from tests.test_context import XPathContextTest
         from tests.test_xpath1_parser import XPath1ParserTest, LxmlXPath1ParserTest
         from tests.test_xpath2_parser import XPath2ParserTest, LxmlXPath2ParserTest
-        from tests.test_schema_proxy import XPath2ParserXMLSchemaTest, LxmlXPath2ParserXMLSchemaTest
+        if xmlschema is not None:
+            from tests.test_schema_proxy import XPath2ParserXMLSchemaTest, LxmlXPath2ParserXMLSchemaTest
         from tests.test_selectors import XPathSelectorsTest
         from tests.test_package import PackageTest
     except ImportError:
@@ -39,7 +45,8 @@ if __name__ == '__main__':
         from test_context import XPathContextTest
         from test_xpath1_parser import XPath1ParserTest, LxmlXPath1ParserTest
         from test_xpath2_parser import XPath2ParserTest, LxmlXPath2ParserTest
-        from test_schema_proxy import XPath2ParserXMLSchemaTest, LxmlXPath2ParserXMLSchemaTest
+        if xmlschema is not None:
+            from test_schema_proxy import XPath2ParserXMLSchemaTest, LxmlXPath2ParserXMLSchemaTest
         from test_selectors import XPathSelectorsTest
         from test_package import PackageTest
 
diff --git a/tests/test_schema_proxy.py b/tests/test_schema_proxy.py
index 14698c3..fd6db5b 100644
--- a/tests/test_schema_proxy.py
+++ b/tests/test_schema_proxy.py
@@ -43,12 +43,13 @@ except ImportError:
 @unittest.skipIf(xmlschema is None, "xmlschema library required.")
 class XPath2ParserXMLSchemaTest(test_xpath2_parser.XPath2ParserTest):
 
-    schema = xmlschema.XMLSchema('''
-        <!-- Dummy schema for testing proxy API -->
-        <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" targetNamespace="http://xpath.test/ns">
-          <xs:element name="test_element" type="xs:string"/>
-          <xs:attribute name="test_attribute" type="xs:string"/>
-        </xs:schema>''')
+    if xmlschema is not None:
+        schema = xmlschema.XMLSchema('''
+            <!-- Dummy schema for testing proxy API -->
+            <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" targetNamespace="http://xpath.test/ns">
+              <xs:element name="test_element" type="xs:string"/>
+              <xs:attribute name="test_attribute" type="xs:string"/>
+            </xs:schema>''')
 
     def setUp(self):
         self.schema_proxy = XMLSchemaProxy(self.schema)
diff --git a/tests/test_xpath2_parser.py b/tests/test_xpath2_parser.py
index 5ac4faa..90702af 100644
--- a/tests/test_xpath2_parser.py
+++ b/tests/test_xpath2_parser.py
@@ -353,7 +353,6 @@ class XPath2ParserTest(test_xpath1_parser.XPath1ParserTest):
         self.check_value(u"fn:compare('Strasse', 'Straße', 'it_IT')", -1)
         self.check_value(u"fn:compare('Strassen', 'Straße')", 1)
         self.check_value(u"fn:compare('Strasse', 'Straße', 'de_DE')", -1)
-        self.check_value(u"fn:compare('Strasse', 'Straße', 'deutsch')", -1)
 
         with self.assertRaises(locale.Error):
             self.check_value(u"fn:compare('Strasse', 'Straße', 'invalid_collation')")