diff --git a/tests/scripts/set_psa_test_dependencies.py b/tests/scripts/set_psa_test_dependencies.py
index 49716b89af..ec103877f1 100755
--- a/tests/scripts/set_psa_test_dependencies.py
+++ b/tests/scripts/set_psa_test_dependencies.py
@@ -164,7 +164,7 @@ def systematic_dependencies(file_name, function_name, arguments):
     # Run key policy negative tests even if the algorithm to attempt performing
     # is not supported.
     if function_name.endswith('_key_policy') and \
-       arguments[-1] != 'PSA_SUCCESS':
+       arguments[-1].startswith('PSA_ERROR_'):
         arguments[-2] = ''
 
     for arg in arguments:
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 7d64dfedc3..476ad7e655 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -504,19 +504,19 @@ depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR:MBEDTLS
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_RSA_PKCS1V15_SIGN_RAW:PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PKCS1V15_SIGN_RAW:1
 
 PSA key policy: asymmetric signature, wrong algorithm family
-depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR
+depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_RSA_PSS:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256):PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PSS(PSA_ALG_SHA_256):0
 
 PSA key policy: asymmetric signature, wildcard in policy, wrong algorithm family
-depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR
+depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_RSA_PSS:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_ANY_HASH):PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PSS(PSA_ALG_SHA_256):0
 
 PSA key policy: asymmetric signature, wildcard in policy, ECDSA SHA-256
-depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR:MBEDTLS_ECP_DP_SECP256R1_ENABLED
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_ECDSA(PSA_ALG_ANY_HASH):PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"49c9a8c18c4b885638c431cf1df1c994131609b580d4fd43a0cab17db2f13eee":PSA_ALG_ECDSA(PSA_ALG_SHA_256):32
 
 PSA key policy: asymmetric signature, wildcard in policy, PKCS#1v1.5 SHA-256
-depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR:MBEDTLS_MD_C
+depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR:MBEDTLS_MD_C
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_ANY_HASH):PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256):32
 
 PSA key policy: asymmetric signature, wildcard in policy, PKCS#1v1.5 raw
@@ -528,7 +528,7 @@ depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:PSA_ALG_RSA_PKCS1V15_SIGN(PSA_ALG_SHA_256):PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PKCS1V15_SIGN_RAW:0
 
 PSA key policy: asymmetric signature, alg=0 in policy
-depends_on:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR:MBEDTLS_MD_C
+depends_on:PSA_WANT_ALG_RSA_PKCS1V15_SIGN:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR:MBEDTLS_MD_C
 asymmetric_signature_key_policy:PSA_KEY_USAGE_SIGN_HASH | PSA_KEY_USAGE_VERIFY_HASH:0:PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PKCS1V15_SIGN_RAW:0
 
 PSA key policy: asymmetric signature, sign but not verify