diff --git a/include/mbedtls/ssl.h b/include/mbedtls/ssl.h
index c04070d..7110e1c 100644
--- a/include/mbedtls/ssl.h
+++ b/include/mbedtls/ssl.h
@@ -2095,29 +2095,35 @@
  *
  * \param ssl      SSL context
  *
- * \return         0 if successful, MBEDTLS_ERR_SSL_WANT_READ,
- *                 MBEDTLS_ERR_SSL_WANT_WRITE, or a specific SSL error code.
+ * \return         0 if successful, or
+ *                 MBEDTLS_ERR_SSL_WANT_READ or MBEDTLS_ERR_SSL_WANT_WRITE, or
+ *                 MBEDTLS_ERR_SSL_HELLO_VERIFY_REQUIRED (see belowe), or
+ *                 a specific SSL error code.
  *
- * \note           If this function returns non-zero, then the ssl context
+ * \note           If this function returns something other than 0 or
+ *                 MBEDTLS_ERR_SSL_WANT_READ/WRITE, then the ssl context
  *                 becomes unusable, and you should either free it or call
  *                 \c mbedtls_ssl_session_reset() on it before re-using it.
- *                 If DTLS is in use, then you may choose to handle
+ *
+ * \note           If DTLS is in use, then you may choose to handle
  *                 MBEDTLS_ERR_SSL_HELLO_VERIFY_REQUIRED specially for logging
- *                 purposes, but you still need to reset/free the context.
+ *                 purposes, as it is an expected return value rather than an
+ *                 actual error, but you still need to reset/free the context.
  */
 int mbedtls_ssl_handshake( mbedtls_ssl_context *ssl );
 
 /**
  * \brief          Perform a single step of the SSL handshake
  *
- *                 Note: the state of the context (ssl->state) will be at
+ * \note           The state of the context (ssl->state) will be at
  *                 the following state after execution of this function.
  *                 Do not call this function if state is MBEDTLS_SSL_HANDSHAKE_OVER.
  *
  * \param ssl      SSL context
  *
- * \return         0 if successful, MBEDTLS_ERR_SSL_WANT_READ,
- *                 MBEDTLS_ERR_SSL_WANT_WRITE, or a specific SSL error code.
+ * \return         0 if successful, or
+ *                 MBEDTLS_ERR_SSL_WANT_READ or MBEDTLS_ERR_SSL_WANT_WRITE, or
+ *                 a specific SSL error code.
  */
 int mbedtls_ssl_handshake_step( mbedtls_ssl_context *ssl );