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)
 
diff --git a/library/psa_crypto.c b/library/psa_crypto.c
index a8e41a2..406e6c4 100644
--- a/library/psa_crypto.c
+++ b/library/psa_crypto.c
@@ -705,8 +705,8 @@
         return( alg1 );
     /* If the policies are from the same hash-and-sign family, check
      * if one is a wildcard. If so the other has the specific algorithm. */
-    if( PSA_ALG_IS_HASH_AND_SIGN( alg1 ) &&
-        PSA_ALG_IS_HASH_AND_SIGN( alg2 ) &&
+    if( PSA_ALG_IS_SIGN_HASH( alg1 ) &&
+        PSA_ALG_IS_SIGN_HASH( alg2 ) &&
         ( alg1 & ~PSA_ALG_HASH_MASK ) == ( alg2 & ~PSA_ALG_HASH_MASK ) )
     {
         if( PSA_ALG_SIGN_GET_HASH( alg1 ) == PSA_ALG_ANY_HASH )
@@ -808,7 +808,7 @@
     /* If policy_alg is a hash-and-sign with a wildcard for the hash,
      * and requested_alg is the same hash-and-sign family with any hash,
      * then requested_alg is compliant with policy_alg. */
-    if( PSA_ALG_IS_HASH_AND_SIGN( requested_alg ) &&
+    if( PSA_ALG_IS_SIGN_HASH( requested_alg ) &&
         PSA_ALG_SIGN_GET_HASH( policy_alg ) == PSA_ALG_ANY_HASH )
     {
         return( ( policy_alg & ~PSA_ALG_HASH_MASK ) ==
@@ -2698,7 +2698,7 @@
         if( ! PSA_ALG_IS_SIGN_MESSAGE( alg ) )
             return( PSA_ERROR_INVALID_ARGUMENT );
 
-        if ( PSA_ALG_IS_HASH_AND_SIGN( alg ) )
+        if ( PSA_ALG_IS_SIGN_HASH( alg ) )
         {
             if( ! PSA_ALG_IS_HASH( PSA_ALG_SIGN_GET_HASH( alg ) ) )
                 return( PSA_ERROR_INVALID_ARGUMENT );
@@ -2856,7 +2856,7 @@
 {
     psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
 
-    if ( PSA_ALG_IS_HASH_AND_SIGN( alg ) )
+    if ( PSA_ALG_IS_SIGN_HASH( alg ) )
     {
         size_t hash_length;
         uint8_t hash[PSA_HASH_MAX_SIZE];
@@ -2903,7 +2903,7 @@
 {
     psa_status_t status = PSA_ERROR_CORRUPTION_DETECTED;
 
-    if ( PSA_ALG_IS_HASH_AND_SIGN( alg ) )
+    if ( PSA_ALG_IS_SIGN_HASH( alg ) )
     {
         size_t hash_length;
         uint8_t hash[PSA_HASH_MAX_SIZE];
diff --git a/tests/src/psa_exercise_key.c b/tests/src/psa_exercise_key.c
index 923d2c1..91bac67 100644
--- a/tests/src/psa_exercise_key.c
+++ b/tests/src/psa_exercise_key.c
@@ -306,7 +306,7 @@
         psa_algorithm_t hash_alg = PSA_ALG_SIGN_GET_HASH( alg );
 
         /* If the policy allows signing with any hash, just pick one. */
-        if( PSA_ALG_IS_HASH_AND_SIGN( alg ) && hash_alg == PSA_ALG_ANY_HASH )
+        if( PSA_ALG_IS_SIGN_HASH( alg ) && hash_alg == PSA_ALG_ANY_HASH )
         {
     #if defined(KNOWN_SUPPORTED_HASH_ALG)
             hash_alg = KNOWN_SUPPORTED_HASH_ALG;
@@ -925,7 +925,7 @@
 {
     if( PSA_ALG_IS_MAC( alg ) || PSA_ALG_IS_SIGN( alg ) )
     {
-        if( PSA_ALG_IS_HASH_AND_SIGN( alg ) )
+        if( PSA_ALG_IS_SIGN_HASH( alg ) )
         {
             if( PSA_ALG_SIGN_GET_HASH( alg ) )
                 return( PSA_KEY_TYPE_IS_PUBLIC_KEY( type ) ?
diff --git a/tests/suites/test_suite_psa_crypto.function b/tests/suites/test_suite_psa_crypto.function
index 5fa45d8..2eab8e5 100644
--- a/tests/suites/test_suite_psa_crypto.function
+++ b/tests/suites/test_suite_psa_crypto.function
@@ -1159,7 +1159,7 @@
     else
         TEST_EQUAL( status, PSA_ERROR_NOT_PERMITTED );
 
-    if( PSA_ALG_IS_HASH_AND_SIGN( exercise_alg ) &&
+    if( PSA_ALG_IS_SIGN_HASH( exercise_alg ) &&
         PSA_ALG_IS_HASH( PSA_ALG_SIGN_GET_HASH( exercise_alg ) ) )
     {
         status = psa_sign_message( key, exercise_alg,
diff --git a/tests/suites/test_suite_psa_crypto_metadata.data b/tests/suites/test_suite_psa_crypto_metadata.data
index 1ea8e63..89705e8 100644
--- a/tests/suites/test_suite_psa_crypto_metadata.data
+++ b/tests/suites/test_suite_psa_crypto_metadata.data
@@ -212,31 +212,31 @@
 
 Asymmetric signature: RSA PKCS#1 v1.5 raw
 depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN
-asymmetric_signature_algorithm:PSA_ALG_RSA_PKCS1V15_SIGN_RAW:ALG_IS_RSA_PKCS1V15_SIGN | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_RSA_PKCS1V15_SIGN_RAW:ALG_IS_RSA_PKCS1V15_SIGN | ALG_IS_SIGN_HASH
 
 Asymmetric signature: RSA PKCS#1 v1.5 SHA-256
 depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_SHA_256
-asymmetric_signature_algorithm:PSA_ALG_RSA_PKCS1V15_SIGN( PSA_ALG_SHA_256 ):ALG_IS_RSA_PKCS1V15_SIGN | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_RSA_PKCS1V15_SIGN( PSA_ALG_SHA_256 ):ALG_IS_RSA_PKCS1V15_SIGN | ALG_IS_SIGN_HASH
 
 Asymmetric signature: RSA PSS SHA-256
 depends_on:PSA_WANT_ALG_RSA_PSS:PSA_WANT_ALG_SHA_256
-asymmetric_signature_algorithm:PSA_ALG_RSA_PSS( PSA_ALG_SHA_256 ):ALG_IS_RSA_PSS | ALG_IS_RSA_PSS_STANDARD_SALT | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_RSA_PSS( PSA_ALG_SHA_256 ):ALG_IS_RSA_PSS | ALG_IS_RSA_PSS_STANDARD_SALT | ALG_IS_SIGN_HASH
 
 Asymmetric signature: RSA PSS-any-salt SHA-256
 depends_on:PSA_WANT_ALG_RSA_PSS:PSA_WANT_ALG_SHA_256
-asymmetric_signature_algorithm:PSA_ALG_RSA_PSS_ANY_SALT( PSA_ALG_SHA_256 ):ALG_IS_RSA_PSS | ALG_IS_RSA_PSS_ANY_SALT | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_RSA_PSS_ANY_SALT( PSA_ALG_SHA_256 ):ALG_IS_RSA_PSS | ALG_IS_RSA_PSS_ANY_SALT | ALG_IS_SIGN_HASH
 
 Asymmetric signature: randomized ECDSA (no hashing)
 depends_on:PSA_WANT_ALG_ECDSA
-asymmetric_signature_algorithm:PSA_ALG_ECDSA_ANY:ALG_IS_ECDSA | ALG_IS_RANDOMIZED_ECDSA | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_ECDSA_ANY:ALG_IS_ECDSA | ALG_IS_RANDOMIZED_ECDSA | ALG_IS_SIGN_HASH
 
 Asymmetric signature: SHA-256 + randomized ECDSA
 depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256
-asymmetric_signature_algorithm:PSA_ALG_ECDSA( PSA_ALG_SHA_256 ):ALG_IS_ECDSA | ALG_IS_RANDOMIZED_ECDSA | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_ECDSA( PSA_ALG_SHA_256 ):ALG_IS_ECDSA | ALG_IS_RANDOMIZED_ECDSA | ALG_IS_SIGN_HASH
 
 Asymmetric signature: SHA-256 + deterministic ECDSA using SHA-256
 depends_on:PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_ALG_SHA_256
-asymmetric_signature_algorithm:PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):ALG_IS_ECDSA | ALG_IS_DETERMINISTIC_ECDSA | ALG_ECDSA_IS_DETERMINISTIC | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_DETERMINISTIC_ECDSA( PSA_ALG_SHA_256 ):ALG_IS_ECDSA | ALG_IS_DETERMINISTIC_ECDSA | ALG_ECDSA_IS_DETERMINISTIC | ALG_IS_SIGN_HASH
 
 Asymmetric signature: pure EdDSA
 depends_on:PSA_WANT_ALG_EDDSA
@@ -244,11 +244,11 @@
 
 Asymmetric signature: Ed25519ph
 depends_on:PSA_WANT_ALG_EDDSA
-asymmetric_signature_algorithm:PSA_ALG_ED25519PH:ALG_IS_HASH_EDDSA | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_ED25519PH:ALG_IS_HASH_EDDSA | ALG_IS_SIGN_HASH
 
 Asymmetric signature: Ed448ph
 depends_on:PSA_WANT_ALG_EDDSA
-asymmetric_signature_algorithm:PSA_ALG_ED448PH:ALG_IS_HASH_EDDSA | ALG_IS_HASH_AND_SIGN
+asymmetric_signature_algorithm:PSA_ALG_ED448PH:ALG_IS_HASH_EDDSA | ALG_IS_SIGN_HASH
 
 Asymmetric signature: RSA PKCS#1 v1.5 with wildcard hash
 depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN
diff --git a/tests/suites/test_suite_psa_crypto_metadata.function b/tests/suites/test_suite_psa_crypto_metadata.function
index 827ad1b..e6d2127 100644
--- a/tests/suites/test_suite_psa_crypto_metadata.function
+++ b/tests/suites/test_suite_psa_crypto_metadata.function
@@ -33,7 +33,7 @@
 #define ALG_IS_DETERMINISTIC_ECDSA      ( 1u << 14 )
 #define ALG_IS_RANDOMIZED_ECDSA         ( 1u << 15 )
 #define ALG_IS_HASH_EDDSA               ( 1u << 16 )
-#define ALG_IS_HASH_AND_SIGN            ( 1u << 17 )
+#define ALG_IS_SIGN_HASH            ( 1u << 17 )
 #define ALG_IS_RSA_OAEP                 ( 1u << 18 )
 #define ALG_IS_HKDF                     ( 1u << 19 )
 #define ALG_IS_FFDH                     ( 1u << 20 )
@@ -114,7 +114,7 @@
     TEST_CLASSIFICATION_MACRO( ALG_IS_DETERMINISTIC_ECDSA, alg, flags );
     TEST_CLASSIFICATION_MACRO( ALG_IS_RANDOMIZED_ECDSA, alg, flags );
     TEST_CLASSIFICATION_MACRO( ALG_IS_HASH_EDDSA, alg, flags );
-    TEST_CLASSIFICATION_MACRO( ALG_IS_HASH_AND_SIGN, alg, flags );
+    TEST_CLASSIFICATION_MACRO( ALG_IS_SIGN_HASH, alg, flags );
     TEST_CLASSIFICATION_MACRO( ALG_IS_RSA_OAEP, alg, flags );
     TEST_CLASSIFICATION_MACRO( ALG_IS_HKDF, alg, flags );
     TEST_CLASSIFICATION_MACRO( ALG_IS_WILDCARD, alg, flags );
@@ -485,7 +485,7 @@
 /* BEGIN_CASE */
 void asymmetric_signature_wildcard( int alg_arg, int classification_flags )
 {
-    classification_flags |= ALG_IS_HASH_AND_SIGN | ALG_IS_WILDCARD;
+    classification_flags |= ALG_IS_SIGN_HASH | ALG_IS_WILDCARD;
     test_asymmetric_signature_algorithm( alg_arg, classification_flags );
     /* Any failure of this test function comes from
      * asymmetric_signature_algorithm. Pacify -Werror=unused-label. */