diff --git a/README.md b/README.md
index 6c4fdac..4afb9c0 100644
--- a/README.md
+++ b/README.md
@@ -210,27 +210,6 @@ 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.
@@ -391,6 +370,52 @@ JupyterHub create local accounts using the LDAPAuthenticator.
 Issue [#19](https://github.com/jupyterhub/ldapauthenticator/issues/19) provides
 additional discussion on local user creation.
 
+## Handling SSL/TLS handshake errors
+
+If you have received a SSL/TLS handshake error, it could be that no [cipher
+suit] accepted by LDAPAuthenticator is also accepted by the LDAP server. This is
+likely because LDAPAuthenticator is stricter than the LDAP server and only
+accepts modern ciphers than the LDAP server doesn't accept. Due to this, you
+should from a security perspective ideally modernize the LDAP server's accepted
+cipher suites rather than expand the LDAPAuthenticator accepted cipher suites to
+include older cipher suites.
+
+LDAPAuthenticator cipher suites accepted by default stem from
+[ssl.create_default_context().get_ciphers()], which makes them dependent on the
+Python version. Upgrading Python from 3.7 - 3.9 to 3.10 - 3.13 is known to
+strictly reduce the set of accepted cipher suites from 30 to 17 for example. Due
+to this, upgrading Python could lead to observing a handshake error previously
+not observed.
+
+If you want to configure LDAPAuthenticator to accept older cipher suites instead
+of updating the LDAP server to accept modern cipher suites, you can do it using
+`LDAPAuthenticator.tls_kwargs`.
+
+```python
+# default ciphers accepted by LDAPAuthenticator in Python 3.7 - 3.9
+# it includes 30 ciphers, where 13 of them were considered less
+# secure and removed in Python 3.10+
+old_ciphers_list_considered_less_secure = "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 by LDAPAuthenticator in Python 3.10 - 3.13
+# it includes 17 ciphers out of the 30 in the old ciphers list
+new_ciphers_list = "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": old_ciphers_list_considered_less_secure,
+}
+```
+
+For reference, you can use a command like below to see what the default cipher
+suites LDAPAuthenticator will use in various Python versions.
+
+```shell
+docker run -it --rm python:3.13 python -c 'import ssl; c = ssl.create_default_context(); print(":".join(sorted([c["name"] for c in c.get_ciphers()])))'
+```
+
+[cipher suite]: https://en.wikipedia.org/wiki/Cipher_suite#Full_handshake:_coordinating_cipher_suites
+[ssl.create_default_context().get_ciphers()]: https://docs.python.org/3/library/ssl.html#ssl.create_default_context
+
 ## Testing LDAPAuthenticator without JupyterHub
 
 This script can be written to a file such as `test_ldap_auth.py`, and run with