diff --git a/library/ssl_client.c b/library/ssl_client.c
index f20542e318..eeb586db2f 100644
--- a/library/ssl_client.c
+++ b/library/ssl_client.c
@@ -621,15 +621,6 @@ static int ssl_write_client_hello_body( mbedtls_ssl_context *ssl,
      * Random random;
      * ...
      *
-     * with for TLS 1.2
-     * struct {
-     *     uint32 gmt_unix_time;
-     *     opaque random_bytes[28];
-     * } Random;
-     *
-     * and for TLS 1.3
-     * opaque Random[32];
-     *
      * The random bytes have been prepared by ssl_prepare_client_hello() into
      * the handshake->randbytes buffer and are copied here into the output
      * buffer.
@@ -652,7 +643,7 @@ static int ssl_write_client_hello_body( mbedtls_ssl_context *ssl,
      * opaque legacy_session_id<0..32>;
      * ...
      *
-     * The (legacy) session identifier bytes have been by
+     * The (legacy) session identifier bytes have been prepared by
      * ssl_prepare_client_hello() into the ssl->session_negotiate->id buffer
      * and are copied here into the output buffer.
      */
@@ -890,9 +881,9 @@ static int ssl_prepare_client_hello( mbedtls_ssl_context *ssl )
     }
 
     /*
-     * But when responding to a verify request where we MUST reuse the
-     * previoulsy generated random bytes (RFC 6347 4.2.1), generate the
-     * random bytes.
+     * Generate the random bytes, except when responding to a verify request
+     * where we MUST reuse the previoulsy generated random bytes
+     * (RFC 6347 4.2.1).
      */
 #if defined(MBEDTLS_SSL_PROTO_DTLS)
     if( ( ssl->conf->transport != MBEDTLS_SSL_TRANSPORT_DATAGRAM ) ||
@@ -908,9 +899,10 @@ static int ssl_prepare_client_hello( mbedtls_ssl_context *ssl )
     }
 
     /*
-     * Prepare session identifier. But in the case of a TLS 1.2 session
-     * renegotiation or session resumption, the initial value of the session
-     * identifier length below is equal to zero.
+     * Prepare session identifier. At that point, the length of the session
+     * identifier in the SSL context `ssl->session_negotiate->id_len` is equal
+     * to zero, except in the case of a TLS 1.2 session renegotiation or
+     * session resumption.
      */
     session_id_len = ssl->session_negotiate->id_len;
 
@@ -1019,7 +1011,7 @@ int mbedtls_ssl_write_client_hello( mbedtls_ssl_context *ssl )
          * The two functions below may try to send data on the network and
          * can return with the MBEDTLS_ERR_SSL_WANT_READ error code when they
          * fail to do so and the transmission has to be retried later. In that
-         * case as in fatal error cases, we return immediatly. But we must have
+         * case as in fatal error cases, we return immediately. But we must have
          * set the handshake state to the next state at that point to ensure
          * that we will not write and send again a ClientHello when we
          * eventually succeed in sending the pending data.
diff --git a/library/ssl_tls13_client.c b/library/ssl_tls13_client.c
index 97cf61bbb9..58aac471e9 100644
--- a/library/ssl_tls13_client.c
+++ b/library/ssl_tls13_client.c
@@ -714,6 +714,18 @@ int mbedtls_ssl_tls13_write_client_hello_exts( mbedtls_ssl_context *ssl,
 /*
  * Functions for parsing and processing Server Hello
  */
+/**
+ * \brief Detect if the ServerHello contains a supported_versions extension
+ *        or not.
+ *
+ * \param[in] ssl  SSL context
+ * \param[in] buf  Buffer containing the ServerHello message
+ * \param[in] end  End of the buffer containing the ServerHello message
+ *
+ * \return 0 if the ServerHello does not contain a supported_versions extension
+ * \return 1 if the ServerHello contains a supported_versions extension
+ * \return A negative value if an error occurred while parsing the ServerHello.
+ */
 static int ssl_tls13_is_supported_versions_ext_present(
     mbedtls_ssl_context *ssl,
     const unsigned char *buf,
@@ -726,10 +738,10 @@ static int ssl_tls13_is_supported_versions_ext_present(
 
     /*
      * Check there is enough data to access the legacy_session_id_echo vector
-     * length.
-     * - legacy_version,         2 bytes
-     * - random                  MBEDTLS_SERVER_HELLO_RANDOM_LEN bytes
-     * - legacy_session_id_echo  1 byte
+     * length:
+     * - legacy_version                 2 bytes
+     * - random                         MBEDTLS_SERVER_HELLO_RANDOM_LEN bytes
+     * - legacy_session_id_echo length  1 byte
      */
     MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, MBEDTLS_SERVER_HELLO_RANDOM_LEN + 3 );
     p += MBEDTLS_SERVER_HELLO_RANDOM_LEN + 2;