diff --git a/include/mbedtls/ssl.h b/include/mbedtls/ssl.h
index e837f4ceb4..541fcc8e6f 100644
--- a/include/mbedtls/ssl.h
+++ b/include/mbedtls/ssl.h
@@ -1442,12 +1442,27 @@ struct mbedtls_ssl_context {
      *
      * Also used on clients for SNI.
      *
-     * If this is \p NULL, the peer name verification is skipped, and
-     * the server_name extension is not sent.
+     * The value of this field can be:
+     * - \p NULL in a newly initialized or reset context.
+     * - A heap-allocated copy of the last value passed to
+     *   mbedtls_ssl_set_hostname(), if the last call had a non-null
+     *  \p hostname argument.
+     * - A special value to indicate that mbedtls_ssl_set_hostname()
+     *   was called with \p NULL (as opposed to never having been called).
+     *   See `mbedtls_ssl_get_hostname_pointer()` in `ssl_tls.c`.
      *
-     * This can be a special value to indicate that mbedtls_ssl_set_hostname()
-     * has been called with \p NULL, as opposed to never having been called.
-     * See mbedtls_ssl_get_hostname_pointer().
+     * If this field contains the value \p NULL and the configuration option
+     * #MBEDTLS_SSL_CLI_ALLOW_WEAK_CERTIFICATE_VERIFICATION_WITHOUT_HOSTNAME
+     * is unset, on a TLS client, attempting to verify a server certificate
+     * results in the error
+     * #MBEDTLS_ERR_SSL_CERTIFICATE_VERIFICATION_WITHOUT_HOSTNAME.
+     *
+     * If this field contains the special value described above, or if
+     * the value is \p NULL and the configuration option
+     * #MBEDTLS_SSL_CLI_ALLOW_WEAK_CERTIFICATE_VERIFICATION_WITHOUT_HOSTNAME
+     * is set, then the peer name verification is skipped, which may be
+     * insecure, especially on a client. Furthermore, on a client, the
+     * server_name extension is not sent.
      */
     char *hostname;
 #endif /* MBEDTLS_X509_CRT_PARSE_C */