diff --git a/include/mbedtls/ssl.h b/include/mbedtls/ssl.h
index e294060efa..d9f28d15e0 100644
--- a/include/mbedtls/ssl.h
+++ b/include/mbedtls/ssl.h
@@ -4038,16 +4038,19 @@ void mbedtls_ssl_conf_sig_algs(mbedtls_ssl_config *conf,
 #if defined(MBEDTLS_X509_CRT_PARSE_C)
 /**
  * \brief          Set or reset the hostname to check against the received
- *                 server certificate. It sets the ServerName TLS extension,
- *                 too, if that extension is enabled. (client-side only)
+ *                 peer certificate. On a client, this also sets the
+ *                 ServerName TLS extension, if that extension is enabled.
+ *                 On a TLS 1.3 client, this also sets the server name in
+ *                 the session resumption ticket, if that feature is enabled.
  *
  * \param ssl      SSL context
- * \param hostname the server hostname, may be NULL to clear hostname
-
- * \note           Maximum hostname length MBEDTLS_SSL_MAX_HOST_NAME_LEN.
+ * \param hostname The server hostname. This may be \c NULL to clear
+ *                 the hostname.
  *
- * \return         0 if successful, MBEDTLS_ERR_SSL_ALLOC_FAILED on
- *                 allocation failure, MBEDTLS_ERR_SSL_BAD_INPUT_DATA on
+ * \note           Maximum hostname length #MBEDTLS_SSL_MAX_HOST_NAME_LEN.
+ *
+ * \return         0 if successful, #MBEDTLS_ERR_SSL_ALLOC_FAILED on
+ *                 allocation failure, #MBEDTLS_ERR_SSL_BAD_INPUT_DATA on
  *                 too long input hostname.
  *
  *                 Hostname set to the one provided on success (cleared