diff --git a/tests/scripts/analyze_outcomes.py b/tests/scripts/analyze_outcomes.py
index 18c8bde..09e1245 100755
--- a/tests/scripts/analyze_outcomes.py
+++ b/tests/scripts/analyze_outcomes.py
@@ -206,6 +206,11 @@
             'PBES2 Encrypt, pad=6 (PKCS7 padding disabled)',
             'PBES2 Encrypt, pad=8 (PKCS7 padding disabled)',
         ],
+        'test_suite_psa_crypto': [
+            # We don't test this unusual, but sensible configuration.
+            # https://github.com/Mbed-TLS/mbedtls/issues/9592
+            re.compile(r'.*ECDSA.*only deterministic supported'),
+        ],
         'test_suite_psa_crypto_generate_key.generated': [
             # Ignore mechanisms that are not implemented, except
             # for public keys for which we always test that
@@ -258,6 +263,9 @@
             # "PSA test case generation: dependency inference class: operation fail"
             # from https://github.com/Mbed-TLS/mbedtls/pull/9025 .
             re.compile(r'.* with (?:DH|ECC)_(?:KEY_PAIR|PUBLIC_KEY)\(.*'),
+            # We don't test this unusual, but sensible configuration.
+            # https://github.com/Mbed-TLS/mbedtls/issues/9592
+            re.compile(r'.*: !ECDSA but DETERMINISTIC_ECDSA with ECC_.*'),
             # PBKDF2_HMAC is not in the default configuration, so we don't
             # enable it in depends.py where we remove hashes.
             # https://github.com/Mbed-TLS/mbedtls/issues/9576
@@ -272,6 +280,11 @@
             # https://github.com/Mbed-TLS/mbedtls/issues/9578
             re.compile(r'PSA sign RSA_PSS_ANY_SALT.*!(?:MD|RIPEMD|SHA).*'),
         ],
+        'test_suite_psa_crypto_op_fail.misc': [
+            # We don't test this unusual, but sensible configuration.
+            # https://github.com/Mbed-TLS/mbedtls/issues/9592
+            'PSA sign DETERMINISTIC_ECDSA(SHA_256): !ECDSA but DETERMINISTIC_ECDSA with ECC_KEY_PAIR(SECP_R1)', #pylint: disable=line-too-long
+        ],
         'test_suite_psa_crypto_storage_format.current': [
             PSA_MECHANISM_NOT_IMPLEMENTED_SEARCH_RE,
         ],
diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 9ac6646..f7bbbc7 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -4735,6 +4735,29 @@
 depends_on:PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_BASIC:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_EXPORT:PSA_WANT_ECC_SECP_R1_384
 verify_hash_interruptible:PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_FAMILY_SECP_R1):"04d9c662b50ba29ca47990450e043aeaf4f0c69b15676d112f622a71c93059af999691c5680d2b44d111579db12f4a413a2ed5c45fcfb67b5b63e00b91ebe59d09a6b1ac2c0c4282aa12317ed5914f999bc488bb132e8342cc36f2ca5e3379c747":PSA_ALG_DETERMINISTIC_ECDSA(PSA_ALG_SHA_256):"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"bed412df472eef873fb0839f91a6867d1c6824d4c5781d4b851faa43c7df904d99dbdd28c0d2fd3a4a006e89d34993a120aff166deb4974e96449a7ffe93c66726ad9443b14b87330c86bdde3faff5fd1cbfdc9afe46f8090376f9664cb116b4":PSA_INTERRUPTIBLE_MAX_OPS_UNLIMITED
 
+# The next 4 test cases check what happens if only one of the two ECDSA
+# variants is supported. The ECDSA variants (deterministic and randomized)
+# are different signature algorithms that can be enabled independently,
+# but they have the same verification. Mbed TLS accepts either variant
+# as the algorithm requested for verification even if that variant is not
+# supported. Test that this works. It would also be acceptable if the
+# library returned NOT_SUPPORTED in this case.
+PSA verify hash: ECDSA SECP256R1, only deterministic supported
+depends_on:!PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY:PSA_WANT_ECC_SECP_R1_256
+verify_hash:PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_FAMILY_SECP_R1):"04dea5e45d0ea37fc566232a508f4ad20ea13d47e4bf5fa4d54a57a0ba012042087097496efc583fed8b24a5b9be9a51de063f5a00a8b698a16fd7f29b5485f320":PSA_ALG_ECDSA_ANY:"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"6a3399f69421ffe1490377adf2ea1f117d81a63cf5bf22e918d51175eb259151ce95d7c26cc04e25503e2f7a1ec3573e3c2412534bb4a19b3a7811742f49f50f"
+
+PSA verify hash with keypair: ECDSA SECP256R1, only deterministic supported
+depends_on:!PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT:PSA_WANT_ECC_SECP_R1_256
+verify_hash:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"ab45435712649cb30bbddac49197eebf2740ffc7f874d9244c3460f54f322d3a":PSA_ALG_ECDSA_ANY:"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"6a3399f69421ffe1490377adf2ea1f117d81a63cf5bf22e918d51175eb259151ce95d7c26cc04e25503e2f7a1ec3573e3c2412534bb4a19b3a7811742f49f50f"
+
+PSA verify hash: deterministic ECDSA SECP256R1, only randomized supported
+depends_on:PSA_WANT_ALG_ECDSA:!PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+verify_hash:PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_FAMILY_SECP_R1):"04dea5e45d0ea37fc566232a508f4ad20ea13d47e4bf5fa4d54a57a0ba012042087097496efc583fed8b24a5b9be9a51de063f5a00a8b698a16fd7f29b5485f320":PSA_ALG_ECDSA_ANY:"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"6a3399f69421ffe1490377adf2ea1f117d81a63cf5bf22e918d51175eb259151ce95d7c26cc04e25503e2f7a1ec3573e3c2412534bb4a19b3a7811742f49f50f"
+
+PSA verify hash with keypair: deterministic ECDSA SECP256R1, only randomized supported
+depends_on:PSA_WANT_ALG_ECDSA:!PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT:PSA_WANT_ECC_SECP_R1_256:PSA_WANT_ALG_SHA_256
+verify_hash:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"ab45435712649cb30bbddac49197eebf2740ffc7f874d9244c3460f54f322d3a":PSA_ALG_DETERMINISTIC_ECDSA(PSA_ALG_SHA_256):"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"6a3399f69421ffe1490377adf2ea1f117d81a63cf5bf22e918d51175eb259151ce95d7c26cc04e25503e2f7a1ec3573e3c2412534bb4a19b3a7811742f49f50f"
+
 PSA verify hash: ECDSA SECP256R1, wrong signature size (correct but ASN1-encoded)
 depends_on:PSA_WANT_ALG_ECDSA:PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY:PSA_WANT_ECC_SECP_R1_256
 verify_hash_fail:PSA_KEY_TYPE_ECC_PUBLIC_KEY(PSA_ECC_FAMILY_SECP_R1):"04dea5e45d0ea37fc566232a508f4ad20ea13d47e4bf5fa4d54a57a0ba012042087097496efc583fed8b24a5b9be9a51de063f5a00a8b698a16fd7f29b5485f320":PSA_ALG_ECDSA_ANY:"9ac4335b469bbd791439248504dd0d49c71349a295fee5a1c68507f45a9e1c7b":"304502206a3399f69421ffe1490377adf2ea1f117d81a63cf5bf22e918d51175eb259151022100ce95d7c26cc04e25503e2f7a1ec3573e3c2412534bb4a19b3a7811742f49f50f":PSA_ERROR_INVALID_SIGNATURE
diff --git a/tests/suites/test_suite_psa_crypto_not_supported.function b/tests/suites/test_suite_psa_crypto_not_supported.function
index f37a197..4f15a3f 100644
--- a/tests/suites/test_suite_psa_crypto_not_supported.function
+++ b/tests/suites/test_suite_psa_crypto_not_supported.function
@@ -26,14 +26,14 @@
 #if defined(PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY)
     if (actual_status == PSA_ERROR_INVALID_ARGUMENT) {
         /* Edge case: when importing an ECC public key with an unspecified
-         * bit-size (as we do here), psa_import_key() infers the bit-size from
-         * the input. If the key type specifies an unknown curve, the validation
-         * might reject the data as invalid before it checks that the curve is
-         * supported. If so, that's ok. In practice, at the time of writing,
-         * this happens with Ed25519, for which a valid but unsupported
-         * 32-byte input causes psa_import_key() to fail because it
-         * assumes a Weierstrass curve which must have an odd-length
-         * encoding.
+         * bit-size (as we do here), the implementation of psa_import_key()
+         * infers the bit-size from the input. If the key type specifies an
+         * unknown curve, the validation might reject the data as invalid
+         * before it checks that the curve is supported. If so, that's ok.
+         * In practice, at the time of writing, this happens with Ed25519,
+         * for which a valid but unsupported 32-byte input causes
+         * psa_import_key() to fail because it assumes a Weierstrass curve
+         * which must have an odd-length encoding.
          *
          * In other cases, we do not expect an INVALID_ARGUMENT error here. */
         TEST_ASSERT(PSA_KEY_TYPE_IS_ECC(key_type));
diff --git a/tests/suites/test_suite_psa_crypto_op_fail.function b/tests/suites/test_suite_psa_crypto_op_fail.function
index 9289869..86e4f1a 100644
--- a/tests/suites/test_suite_psa_crypto_op_fail.function
+++ b/tests/suites/test_suite_psa_crypto_op_fail.function
@@ -252,8 +252,8 @@
     PSA_ASSERT(psa_sign_hash_abort(&sign_operation));
 
     if (!private_only) {
-        /* Determine a plausible signature size to avoid an INVALID_SIGNATURE
-         * error based on this. */
+        /* Construct a signature candidate of a plausible size to avoid an
+         * INVALID_SIGNATURE error based on an early size verification. */
         PSA_ASSERT(psa_get_key_attributes(key_id, &attributes));
         size_t key_bits = psa_get_key_bits(&attributes);
         size_t output_length = sizeof(output);
diff --git a/tests/suites/test_suite_psa_crypto_op_fail.misc.data b/tests/suites/test_suite_psa_crypto_op_fail.misc.data
index 7158f2d..0c69fa8 100644
--- a/tests/suites/test_suite_psa_crypto_op_fail.misc.data
+++ b/tests/suites/test_suite_psa_crypto_op_fail.misc.data
@@ -13,3 +13,24 @@
 PSA sign RSA_PSS(SHA_256): RSA_PSS not enabled, key pair
 depends_on:!PSA_WANT_ALG_RSA_PSS:PSA_WANT_ALG_SHA_256:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC:PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_IMPORT
 sign_fail:PSA_KEY_TYPE_RSA_KEY_PAIR:"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":PSA_ALG_RSA_PSS(PSA_ALG_SHA_256):0:PSA_ERROR_NOT_SUPPORTED
+
+# There is a special case with ECDSA: deterministic and randomized ECDSA are
+# different signature algorithms that can be enabled independently, but
+# the verification algorithms are the same. Mbed TLS supports verification
+# of either variant when either variant is enabled. (It would also be correct
+# to reject the not-supported algorithm, but it would require a few more lines
+# of code.) In the automatically generated test cases, we avoid this difficulty
+# by making the not-supported test cases require neither variant to be
+# enabled. Here, test the signature operation when one variant is supported
+# but not the other. Testing the positive cases for the verification
+# operation is the job of test_suite_psa_crypto.
+#
+# We only test with one curve and one hash, because we know from a gray-box
+# approach that the curve and hash don't matter here.
+PSA sign DETERMINISTIC_ECDSA(SHA_256): !DETERMINISTIC_ECDSA but ECDSA with ECC_KEY_PAIR(SECP_R1)
+depends_on:!PSA_WANT_ALG_DETERMINISTIC_ECDSA:PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_ECC_SECP_R1_192:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT
+sign_fail:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"d83b57a59c51358d9c8bbb898aff507f44dd14cf16917190":PSA_ALG_DETERMINISTIC_ECDSA(PSA_ALG_SHA_256):1:PSA_ERROR_NOT_SUPPORTED
+
+PSA sign DETERMINISTIC_ECDSA(SHA_256): !ECDSA but DETERMINISTIC_ECDSA with ECC_KEY_PAIR(SECP_R1)
+depends_on:PSA_WANT_ALG_DETERMINISTIC_ECDSA:!PSA_WANT_ALG_ECDSA:PSA_WANT_ALG_SHA_256:PSA_WANT_ECC_SECP_R1_192:PSA_WANT_KEY_TYPE_ECC_KEY_PAIR_IMPORT
+sign_fail:PSA_KEY_TYPE_ECC_KEY_PAIR(PSA_ECC_FAMILY_SECP_R1):"d83b57a59c51358d9c8bbb898aff507f44dd14cf16917190":PSA_ALG_ECDSA(PSA_ALG_SHA_256):1:PSA_ERROR_NOT_SUPPORTED