diff --git a/README.md b/README.md
index 76aaba1..6c4fdac 100644
--- a/README.md
+++ b/README.md
@@ -210,6 +210,27 @@ c.LDAPAuthenticator.tls_kwargs = {
 }
 ```
 
+If you have received a TLS handshake error, it could be that no cipher accepted
+by LDAPAuthenticator is also accepted by the LDAP server. The default ciphers
+accepted by LDAPAuthenticator is dependent on the Python version, where
+upgrading to Python 3.10 is known to reduce the set of accepted ciphers. The
+default list of ciphers stem from
+[ssl.create_default_context().get_ciphers()](https://docs.python.org/3/library/ssl.html#ssl.create_default_context).
+
+To configure LDAPAuthenticator's accepted ciphers explicitly, you can do:
+
+```python
+# default ciphers accepted with LDAPAuthenticator in Python < 3.10
+pre_python310_ciphers = "AES128-SHA:AES256-SHA:DHE-RSA-AES128-SHA:DHE-RSA-AES256-SHA:ECDHE-ECDSA-AES128-SHA:ECDHE-ECDSA-AES256-SHA:ECDHE-RSA-AES128-SHA:ECDHE-RSA-AES256-SHA:AES128-GCM-SHA256:AES128-SHA256:AES256-GCM-SHA384:AES256-SHA256:DHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES128-SHA256:DHE-RSA-AES256-GCM-SHA384:DHE-RSA-AES256-SHA256:DHE-RSA-CHACHA20-POLY1305:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-ECDSA-AES256-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-SHA256:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-SHA384:ECDHE-RSA-CHACHA20-POLY1305:TLS_AES_128_GCM_SHA256:TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256"
+
+# default ciphers accepted with LDAPAuthenticator in Python >= 3.10
+post_python310_ciphers = "DHE-RSA-AES128-GCM-SHA256:DHE-RSA-AES128-SHA256:DHE-RSA-AES256-GCM-SHA384:DHE-RSA-AES256-SHA256:ECDHE-ECDSA-AES128-GCM-SHA256:ECDHE-ECDSA-AES128-SHA256:ECDHE-ECDSA-AES256-GCM-SHA384:ECDHE-ECDSA-AES256-SHA384:ECDHE-ECDSA-CHACHA20-POLY1305:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-RSA-AES128-SHA256:ECDHE-RSA-AES256-GCM-SHA384:ECDHE-RSA-AES256-SHA384:ECDHE-RSA-CHACHA20-POLY1305:TLS_AES_128_GCM_SHA256:TLS_AES_256_GCM_SHA384:TLS_CHACHA20_POLY1305_SHA256"
+
+c.LDAPAuthenticator.tls_kwargs = {
+    "ciphers": pre_python310_ciphers,
+}
+```
+
 #### `LDAPAuthenticator.server_port`
 
 Port on which to contact the LDAP server.
diff --git a/ldapauthenticator/ldapauthenticator.py b/ldapauthenticator/ldapauthenticator.py
index 969cf02..5f720a8 100644
--- a/ldapauthenticator/ldapauthenticator.py
+++ b/ldapauthenticator/ldapauthenticator.py
@@ -4,7 +4,7 @@
 
 import ldap3
 from jupyterhub.auth import Authenticator
-from ldap3.core.exceptions import LDAPBindError
+from ldap3.core.exceptions import LDAPBindError, LDAPSocketOpenError
 from ldap3.core.tls import Tls
 from ldap3.utils.conv import escape_filter_chars
 from ldap3.utils.dn import escape_rdn
@@ -536,6 +536,17 @@ def get_connection(self, userdn, password):
                 password=password,
                 auto_bind=auto_bind,
             )
+        except LDAPSocketOpenError as e:
+            if "handshake" in str(e).lower():
+                self.log.error(
+                    "A TLS handshake failure has occurred. "
+                    "It could be an indication that no cipher accepted by "
+                    "LDAPAuthenticator was accepted by the LDAP server. For "
+                    "details on how to handle this, refer to documentation of "
+                    "the tls_kwargs config on how to configure ciphers "
+                    "https://github.com/jupyterhub/ldapauthenticator/#ldapauthenticatortls_kwargs."
+                )
+            raise
         except LDAPBindError as e:
             self.log.debug(
                 "Failed to bind {userdn}\n{e_type}: {e_msg}".format(