diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index 9d6fd44cbc1..a7be4982e00 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -1409,6 +1409,22 @@ def __exit__(self, type_=None, value=None, traceback=None):
 ioerror_peer_reset = TransientResource(OSError, errno=errno.ECONNRESET)
 
 
+def get_socket_conn_refused_errs():
+    """
+    Get the different socket error numbers ('errno') which can be received
+    when a connection is refused.
+    """
+    errors = [errno.ECONNREFUSED]
+    if hasattr(errno, 'ENETUNREACH'):
+        # On Solaris, ENETUNREACH is returned sometimes instead of ECONNREFUSED
+        errors.append(errno.ENETUNREACH)
+    if hasattr(errno, 'EADDRNOTAVAIL'):
+        # bpo-31910: socket.create_connection() fails randomly
+        # with EADDRNOTAVAIL on Travis CI
+        errors.append(errno.EADDRNOTAVAIL)
+    return errors
+
+
 @contextlib.contextmanager
 def transient_internet(resource_name, *, timeout=30.0, errnos=()):
     """Return a context manager that raises ResourceDenied when various issues
diff --git a/Lib/test/test_imaplib.py b/Lib/test/test_imaplib.py
index a060143e1f6..aec36af6c52 100644
--- a/Lib/test/test_imaplib.py
+++ b/Lib/test/test_imaplib.py
@@ -81,14 +81,8 @@ def test_imap4_host_default_value(self):
             except socket.error:
                 pass
 
-        expected_errnos = [
-            # This is the exception that should be raised.
-            errno.ECONNREFUSED,
-        ]
-        if hasattr(errno, 'EADDRNOTAVAIL'):
-            # socket.create_connection() fails randomly with
-            # EADDRNOTAVAIL on Travis CI.
-            expected_errnos.append(errno.EADDRNOTAVAIL)
+        # This is the exception that should be raised.
+        expected_errnos = support.get_socket_conn_refused_errs()
         with self.assertRaises(OSError) as cm:
             imaplib.IMAP4()
         self.assertIn(cm.exception.errno, expected_errnos)
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 38196528961..43929b355e6 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -4720,14 +4720,7 @@ def test_create_connection(self):
         # On Solaris, ENETUNREACH is returned in this circumstance instead
         # of ECONNREFUSED.  So, if that errno exists, add it to our list of
         # expected errnos.
-        expected_errnos = [ errno.ECONNREFUSED, ]
-        if hasattr(errno, 'ENETUNREACH'):
-            expected_errnos.append(errno.ENETUNREACH)
-        if hasattr(errno, 'EADDRNOTAVAIL'):
-            # bpo-31910: socket.create_connection() fails randomly
-            # with EADDRNOTAVAIL on Travis CI
-            expected_errnos.append(errno.EADDRNOTAVAIL)
-
+        expected_errnos = support.get_socket_conn_refused_errs()
         self.assertIn(cm.exception.errno, expected_errnos)
 
     def test_create_connection_timeout(self):
diff --git a/Misc/NEWS.d/next/Tests/2019-04-15-11-57-39.bpo-36629.ySnaL3.rst b/Misc/NEWS.d/next/Tests/2019-04-15-11-57-39.bpo-36629.ySnaL3.rst
new file mode 100644
index 00000000000..0837a233d58
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-04-15-11-57-39.bpo-36629.ySnaL3.rst
@@ -0,0 +1,2 @@
+Fix ``test_imap4_host_default_value()`` of ``test_imaplib``: catch also
+:data:`errno.ENETUNREACH` error.