diff --git a/include/psa/crypto_values.h b/include/psa/crypto_values.h
index 524e2dc..a29beb5 100644
--- a/include/psa/crypto_values.h
+++ b/include/psa/crypto_values.h
@@ -1545,7 +1545,20 @@
  * Hash-and-sign algorithms are asymmetric (public-key) signature algorithms
  * structured in two parts: first the calculation of a hash in a way that
  * does not depend on the key, then the calculation of a signature from the
- * hash value and the key.
+ * hash value and the key. Hash-and-sign algorithms encode the hash
+ * used for the hashing step, and you can call #PSA_ALG_SIGN_GET_HASH
+ * to extract this algorithm.
+ *
+ * Thus, for a hash-and-sign algorithm,
+ * `psa_sign_message(key, alg, input, ...)` is equivalent to
+ * ```
+ * psa_hash_compute(PSA_ALG_SIGN_GET_HASH(alg), input, ..., hash, ...);
+ * psa_sign_hash(key, alg, hash, ..., signature, ...);
+ * ```
+ * Most usefully, separating the hash from the signature allows the hash
+ * to be calculated in multiple steps with psa_hash_setup(), psa_hash_update()
+ * and psa_hash_finish(). Likewise psa_verify_message() is equivalent to
+ * calculating the hash and then calling psa_verify_hash().
  *
  * \param alg An algorithm identifier (value of type #psa_algorithm_t).
  *
@@ -1554,9 +1567,8 @@
  *         algorithm identifier.
  */
 #define PSA_ALG_IS_HASH_AND_SIGN(alg)                                   \
-    (PSA_ALG_IS_RSA_PSS(alg) || PSA_ALG_IS_RSA_PKCS1V15_SIGN(alg) ||    \
-     PSA_ALG_IS_ECDSA(alg) || PSA_ALG_IS_HASH_EDDSA(alg) ||             \
-     PSA_ALG_IS_VENDOR_HASH_AND_SIGN(alg))
+    (PSA_ALG_IS_SIGN_HASH(alg) &&                                       \
+     ((alg) & PSA_ALG_HASH_MASK) != 0)
 
 /** Whether the specified algorithm is a signature algorithm that can be used
  * with psa_sign_message() and psa_verify_message().
@@ -1570,11 +1582,17 @@
  *         supported algorithm identifier.
  */
 #define PSA_ALG_IS_SIGN_MESSAGE(alg)                                    \
-    (PSA_ALG_IS_HASH_AND_SIGN(alg) || (alg) == PSA_ALG_PURE_EDDSA )
+    (PSA_ALG_IS_SIGN_HASH(alg) || (alg) == PSA_ALG_PURE_EDDSA )
 
 /** Whether the specified algorithm is a signature algorithm that can be used
  * with psa_sign_hash() and psa_verify_hash().
  *
+ * This encompasses all strict hash-and-sign algorithms categorized by
+ * PSA_ALG_IS_HASH_AND_SIGN(), as well as algorithms that follow the
+ * paradigm more loosely:
+ * - #PSA_ALG_RSA_PKCS1V15_SIGN_RAW (expects its input to be an encoded hash)
+ * - #PSA_ALG_ECDSA_ANY (doesn't specify what kind of hash the input is)
+ *
  * \param alg An algorithm identifier (value of type psa_algorithm_t).
  *
  * \return 1 if alg is a signature algorithm that can be used to sign a
@@ -1584,8 +1602,9 @@
  *         supported algorithm identifier.
  */
 #define PSA_ALG_IS_SIGN_HASH(alg)                                       \
-    (PSA_ALG_IS_HASH_AND_SIGN(alg) || (alg) == PSA_ALG_ED25519PH ||     \
-    (alg) == PSA_ALG_ED448PH)
+    (PSA_ALG_IS_RSA_PSS(alg) || PSA_ALG_IS_RSA_PKCS1V15_SIGN(alg) ||    \
+     PSA_ALG_IS_ECDSA(alg) || PSA_ALG_IS_HASH_EDDSA(alg) ||             \
+     PSA_ALG_IS_VENDOR_HASH_AND_SIGN(alg))
 
 /** Get the hash used by a hash-and-sign signature algorithm.
  *
@@ -1607,7 +1626,6 @@
  */
 #define PSA_ALG_SIGN_GET_HASH(alg)                                     \
     (PSA_ALG_IS_HASH_AND_SIGN(alg) ?                                   \
-     ((alg) & PSA_ALG_HASH_MASK) == 0 ? /*"raw" algorithm*/ 0 :        \
      ((alg) & PSA_ALG_HASH_MASK) | PSA_ALG_CATEGORY_HASH :             \
      0)