Try this approach

Author: DifferentialOrange

Diff for: appveyor.yml

@@ -1,5 +1,13 @@
 environment:
   matrix:
+    - PYTHON: "C:\\Python27"
+    - PYTHON: "C:\\Python27-x64"
+    - PYTHON: "C:\\Python34"
+    - PYTHON: "C:\\Python34-x64"
+    - PYTHON: "C:\\Python35"
+    - PYTHON: "C:\\Python35-x64"
+    - PYTHON: "C:\\Python36"
+    - PYTHON: "C:\\Python36-x64"
     - PYTHON: "C:\\Python37"
     - PYTHON: "C:\\Python37-x64"
     - PYTHON: "C:\\Python38"

Diff for: tarantool/__init__.py

@@ -1,9 +1,9 @@
 # -*- coding: utf-8 -*-
 # pylint: disable=C0301,W0105,W0401,W0614
 
+import sys
 from tarantool.connection import Connection
 from tarantool.mesh_connection import MeshConnection
-from tarantool.connection_pool import ConnectionPool, Mode
 from tarantool.const import (
     SOCKET_TIMEOUT,
     RECONNECT_MAX_ATTEMPTS,
@@ -76,5 +76,9 @@ def connectmesh(addrs=({'host': 'localhost', 'port': 3301},), user=None,
 
 __all__ = ['connect', 'Connection', 'connectmesh', 'MeshConnection', 'Schema',
            'Error', 'DatabaseError', 'NetworkError', 'NetworkWarning',
-           'SchemaError', 'ConnectionPool',
-           'Mode', 'dbapi']
+           'SchemaError', 'dbapi']
+
+# ConnectionPool is supported only for Python 3.7 or newer.
+if sys.version_info.major >= 3 and sys.version_info.minor >= 7:
+    from tarantool.connection_pool import ConnectionPool, Mode
+    __all__.extend(['ConnectionPool', 'Mode'])

Diff for: test/suites/lib/skip.py

@@ -34,9 +34,8 @@ def wrapper(self, *args, **kwargs):
     return wrapper
 
 
-def skip_or_run_test_python_major(func, REQUIRED_PYTHON_MAJOR, msg):
-    """Decorator to skip or run tests depending on the Python major
-    version.
+def skip_or_run_test_python(func, REQUIRED_PYTHON_VERSION, msg):
+    """Decorator to skip or run tests depending on the Python version.
 
     Also, it can be used with the 'setUp' method for skipping
     the whole test suite.
@@ -47,9 +46,12 @@ def wrapper(self, *args, **kwargs):
         if func.__name__ == 'setUp':
             func(self, *args, **kwargs)
 
-        major = sys.version_info.major
-        if major != REQUIRED_PYTHON_MAJOR:
-            self.skipTest('Python %s connector %s' % (major, msg))
+        ver = sys.version_info
+        python_version_str = '%d.%d' % (ver.major, ver.minor)
+        python_version = pkg_resources.parse_version(python_version_str)
+        support_version = pkg_resources.parse_version(REQUIRED_PYTHON_VERSION)
+        if python_version < support_version:
+            self.skipTest('Python %s connector %s' % (python_version, msg))
 
         if func.__name__ != 'setUp':
             func(self, *args, **kwargs)
@@ -88,4 +90,15 @@ def skip_or_run_mp_bin_test(func):
     Python 2 connector do not support mp_bin.
     """
 
-    return skip_or_run_test_python_major(func, 3, 'does not support mp_bin')
+    return skip_or_run_test_python(func, '3.0', 'does not support mp_bin')
+
+
+def skip_or_run_conn_pool_test(func):
+    """Decorator to skip or run mp_bin-related tests depending on
+    the Python version.
+
+    Python 2 connector do not support mp_bin.
+    """
+
+    return skip_or_run_test_python(func, '3.7',
+                                   'does not support ConnectionPool')

Diff for: test/suites/test_pool.py

@@ -11,6 +11,7 @@
 import tarantool
 from tarantool.error import ClusterTolopogyError, DatabaseError, NetworkError
 
+from .lib.skip import skip_or_run_conn_pool_test
 from .lib.tarantool_server import TarantoolServer
 
 
@@ -71,6 +72,7 @@ def setUpClass(self):
         print(' POOL '.center(70, '='), file=sys.stderr)
         print('-' * 70, file=sys.stderr)
 
+    @skip_or_run_conn_pool_test
     def setUp(self):
         # Create five servers and extract helpful fields for tests.
         self.servers = []