diff --git a/scripts/mbedtls_dev/crypto_knowledge.py b/scripts/mbedtls_dev/crypto_knowledge.py
index 5e579ce..4e9503e 100644
--- a/scripts/mbedtls_dev/crypto_knowledge.py
+++ b/scripts/mbedtls_dev/crypto_knowledge.py
@@ -212,9 +212,7 @@
         This function does not currently handle key derivation or PAKE.
         """
         #pylint: disable=too-many-branches,too-many-return-statements
-        if alg.is_wildcard:
-            return False
-        if alg.is_invalid_truncation():
+        if not alg.is_valid_for_operation():
             return False
         if self.head == 'HMAC' and alg.head == 'HMAC':
             return True
@@ -495,6 +493,19 @@
                 return True
         return False
 
+    def is_valid_for_operation(self) -> bool:
+        """Whether this algorithm construction is valid for an operation.
+
+        This function assumes that the algorithm is constructed in a
+        "grammatically" correct way, and only rejects semantically invalid
+        combinations.
+        """
+        if self.is_wildcard:
+            return False
+        if self.is_invalid_truncation():
+            return False
+        return True
+
     def can_do(self, category: AlgorithmCategory) -> bool:
         """Whether this algorithm can perform operations in the given category.
         """
diff --git a/tests/scripts/generate_psa_tests.py b/tests/scripts/generate_psa_tests.py
index 0f37889..f5b921e 100755
--- a/tests/scripts/generate_psa_tests.py
+++ b/tests/scripts/generate_psa_tests.py
@@ -151,8 +151,8 @@
     tc.set_arguments([key_type] + list(args))
     return tc
 
-class NotSupported:
-    """Generate test cases for when something is not supported."""
+class KeyTypeNotSupported:
+    """Generate test cases for when a key type is not supported."""
 
     def __init__(self, info: Information) -> None:
         self.constructors = info.constructors
@@ -521,7 +521,7 @@
             key_type: psa_storage.Expr, bits: int,
             alg: psa_storage.Expr
     ) -> bool:
-        """Whether to the given key with the given algorithm.
+        """Whether to exercise the given key with the given algorithm.
 
         Normally only the type and algorithm matter for compatibility, and
         this is handled in crypto_knowledge.KeyType.can_do(). This function
@@ -902,7 +902,7 @@
         'test_suite_psa_crypto_generate_key.generated':
         lambda info: KeyGenerate(info).test_cases_for_key_generation(),
         'test_suite_psa_crypto_not_supported.generated':
-        lambda info: NotSupported(info).test_cases_for_not_supported(),
+        lambda info: KeyTypeNotSupported(info).test_cases_for_not_supported(),
         'test_suite_psa_crypto_op_fail.generated':
         lambda info: OpFail(info).all_test_cases(),
         'test_suite_psa_crypto_storage_format.current':