diff --git a/include/psa/crypto.h b/include/psa/crypto.h
index d3b7522..7291c3e 100644
--- a/include/psa/crypto.h
+++ b/include/psa/crypto.h
@@ -459,9 +459,12 @@
  * maintain the key handle until after the multipart operation has finished.
  *
  * \param handle        The key handle to close.
+ *                      If this is \c 0, do nothing and return \c PSA_SUCCESS.
  *
  * \retval #PSA_SUCCESS
+ *         \p handle was a valid handle or \c 0. It is now closed.
  * \retval #PSA_ERROR_INVALID_HANDLE
+ *         \p handle is not a valid handle nor \c 0.
  * \retval #PSA_ERROR_COMMUNICATION_FAILURE
  * \retval #PSA_ERROR_CORRUPTION_DETECTED
  * \retval #PSA_ERROR_BAD_STATE
@@ -579,13 +582,17 @@
  * key will cause the multipart operation to fail.
  *
  * \param handle        Handle to the key to erase.
+ *                      If this is \c 0, do nothing and return \c PSA_SUCCESS.
  *
  * \retval #PSA_SUCCESS
- *         The key material has been erased.
+ *         \p handle was a valid handle and the key material that it
+ *         referred to has been erased.
+ *         Alternatively, \p handle is \c 0.
  * \retval #PSA_ERROR_NOT_PERMITTED
  *         The key cannot be erased because it is
  *         read-only, either due to a policy or due to physical restrictions.
  * \retval #PSA_ERROR_INVALID_HANDLE
+ *         \p handle is not a valid handle nor \c 0.
  * \retval #PSA_ERROR_COMMUNICATION_FAILURE
  *         There was an failure in communication with the cryptoprocessor.
  *         The key material may still be present in the cryptoprocessor.