diff --git a/include/psa/crypto.h b/include/psa/crypto.h
index 51a2b0e..e87892b 100644
--- a/include/psa/crypto.h
+++ b/include/psa/crypto.h
@@ -852,12 +852,13 @@
  *
  * The policy on the source key must have the usage flag
  * #PSA_KEY_USAGE_COPY set.
- * In addition, some lifetimes also require the source key to have the
- * usage flag #PSA_KEY_USAGE_EXPORT, because otherwise the source key
- * is locked inside a secure processing environment and cannot be
- * extracted. For keys with the lifetime #PSA_KEY_LIFETIME_VOLATILE or
- * #PSA_KEY_LIFETIME_PERSISTENT, the usage flag #PSA_KEY_USAGE_COPY
- * is sufficient to permit the copy.
+ * This flag is sufficient to permit the copy if the key has the lifetime
+ * #PSA_KEY_LIFETIME_VOLATILE or #PSA_KEY_LIFETIME_PERSISTENT.
+ * Some secure elements do not provide a way to copy a key without
+ * making it extractable from the secure element. If a key is located
+ * in such a secure element, then the key must have both usage flags
+ * #PSA_KEY_USAGE_COPY and #PSA_KEY_USAGE_EXPORT in order to make
+ * a copy of the key outside the secure element.
  *
  * The resulting key may only be used in a way that conforms to
  * both the policy of the original key and the policy specified in
diff --git a/include/psa/crypto_values.h b/include/psa/crypto_values.h
index 766e396..fa0d14d 100644
--- a/include/psa/crypto_values.h
+++ b/include/psa/crypto_values.h
@@ -1461,13 +1461,15 @@
 
 /** Whether the key may be copied.
  *
- * This flag allows the use of psa_crypto_copy() to make a copy of the key
+ * This flag allows the use of psa_copy_key() to make a copy of the key
  * with the same policy or a more restrictive policy.
  *
- * For some lifetimes, copying a key also requires the usage flag
- * #PSA_KEY_USAGE_EXPORT, because otherwise the source key
- * is locked inside a secure processing environment and cannot be
- * extracted. For keys with the lifetime #PSA_KEY_LIFETIME_VOLATILE or
+ * For lifetimes for which the key is located in a secure element which
+ * enforce the non-exportability of keys, copying a key outside the secure
+ * element also requires the usage flag #PSA_KEY_USAGE_EXPORT.
+ * Copying the key inside the secure element is permitted with just
+ * #PSA_KEY_USAGE_COPY if the secure element supports it.
+ * For keys with the lifetime #PSA_KEY_LIFETIME_VOLATILE or
  * #PSA_KEY_LIFETIME_PERSISTENT, the usage flag #PSA_KEY_USAGE_COPY
  * is sufficient to permit the copy.
  */