diff --git a/tests/suites/test_suite_psa_crypto.data b/tests/suites/test_suite_psa_crypto.data
index 307b2c171..06b1ebae2 100644
--- a/tests/suites/test_suite_psa_crypto.data
+++ b/tests/suites/test_suite_psa_crypto.data
@@ -357,11 +357,9 @@ depends_on:MBEDTLS_AES_C
 import_with_data:"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa":PSA_KEY_TYPE_AES:128:PSA_ERROR_INVALID_ARGUMENT
 
 PSA import large key: raw, 65528 bits (ok)
-depends_on:HAVE_RAM_AVAILABLE_128K
 import_large_key:PSA_KEY_TYPE_RAW_DATA:8191:PSA_SUCCESS
 
 PSA import large key: raw, 65536 bits (not supported)
-depends_on:HAVE_RAM_AVAILABLE_128K
 import_large_key:PSA_KEY_TYPE_RAW_DATA:8192:PSA_ERROR_NOT_SUPPORTED
 
 PSA import RSA key pair: maximum size exceeded
@@ -2520,8 +2518,8 @@ derive_key:PSA_ALG_HKDF(PSA_ALG_SHA_256):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b
 # and not expected to be raised any time soon) is less than the maximum
 # output from HKDF-SHA512 (255*64 = 16320 bytes).
 PSA key derivation: largest possible key
-depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_512:HAVE_RAM_AVAILABLE_128K
-derive_key:PSA_ALG_HKDF(PSA_ALG_SHA_512):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_RAW_DATA:PSA_MAX_KEY_BITS:PSA_SUCCESS
+depends_on:PSA_WANT_ALG_HKDF:PSA_WANT_ALG_SHA_512
+derive_large_key:PSA_ALG_HKDF(PSA_ALG_SHA_512):"0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b":"000102030405060708090a0b0c":"f0f1f2f3f4f5f6f7f8f9":PSA_KEY_TYPE_RAW_DATA:PSA_MAX_KEY_BITS:PSA_SUCCESS
 
 PSA key derivation: key too large
 depends_on:MBEDTLS_SHA512_C
@@ -2679,8 +2677,7 @@ PSA generate key: raw data, (2 * MBEDTLS_CTR_DRBG_MAX_REQUEST + 1) * 8 bits
 generate_key:PSA_KEY_TYPE_RAW_DATA:(2 * MBEDTLS_CTR_DRBG_MAX_REQUEST + 1) * 8:PSA_KEY_USAGE_EXPORT:0:PSA_SUCCESS
 
 PSA generate key: raw data, 65528 bits (ok)
-depends_on:HAVE_RAM_AVAILABLE_128K
-generate_key:PSA_KEY_TYPE_RAW_DATA:65528:PSA_KEY_USAGE_EXPORT:0:PSA_SUCCESS
+generate_large_key:PSA_KEY_TYPE_RAW_DATA:65528:PSA_KEY_USAGE_EXPORT:0:PSA_SUCCESS
 
 PSA generate key: raw data, 65536 bits (not supported)
 generate_key:PSA_KEY_TYPE_RAW_DATA:65536:PSA_KEY_USAGE_EXPORT:0:PSA_ERROR_NOT_SUPPORTED
diff --git a/tests/suites/test_suite_psa_crypto.function b/tests/suites/test_suite_psa_crypto.function
index a65c482a5..061c52e5e 100644
--- a/tests/suites/test_suite_psa_crypto.function
+++ b/tests/suites/test_suite_psa_crypto.function
@@ -9,13 +9,6 @@
  * uses mbedtls_ctr_drbg internally. */
 #include "mbedtls/ctr_drbg.h"
 
-/* Tests that require more than 128kB of RAM plus change have this symbol
- * as a dependency. Currently we always define this symbol, so the tests
- * are always executed. In the future we should make this conditional
- * so that tests that require a lot of memory are skipped on constrained
- * platforms. */
-#define HAVE_RAM_AVAILABLE_128K
-
 #include "psa/crypto.h"
 #include "psa_crypto_slot_management.h"
 
@@ -1588,9 +1581,9 @@ void import_large_key( int type_arg, int byte_size_arg,
     size_t buffer_size = byte_size + 1;
     size_t n;
 
-    /* It would be better to skip the test than fail it if the allocation
-     * fails, but the test framework doesn't support this yet. */
-    ASSERT_ALLOC( buffer, buffer_size );
+    /* Skip the test case if the target running the test cannot
+     * accomodate large keys due to heap size constraints */
+    ASSERT_ALLOC_WEAK( buffer, buffer_size );
     memset( buffer, 'K', byte_size );
 
     PSA_ASSERT( psa_crypto_init( ) );
@@ -5332,6 +5325,26 @@ exit:
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void derive_large_key( int alg_arg,
+                       data_t *key_data, data_t *input1, data_t *input2,
+                       int type_arg, int bits_arg,
+                       int expected_status_arg )
+{
+    size_t key_bytes = PSA_BITS_TO_BYTES(bits_arg);
+    uint8_t* buffer = NULL;
+
+    /* Check that the target running this test can accomodate large
+     * keys on its heap, before calling the actual generate_key test */
+    ASSERT_ALLOC_WEAK(buffer, key_bytes);
+    mbedtls_free( buffer );
+
+    test_derive_key( alg_arg, key_data, input1, input2, type_arg, bits_arg, expected_status_arg );
+exit:
+    return;
+}
+/* END_CASE */
+
 /* BEGIN_CASE */
 void key_agreement_setup( int alg_arg,
                           int our_key_type_arg, int our_key_alg_arg,
@@ -5640,6 +5653,27 @@ exit:
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void generate_large_key( int type_arg,
+                         int bits_arg,
+                         int usage_arg,
+                         int alg_arg,
+                         int expected_status_arg )
+{
+    size_t key_bytes = PSA_BITS_TO_BYTES(bits_arg);
+    uint8_t* buffer = NULL;
+
+    /* Check that the target running this test can accomodate large
+     * keys on its heap, before calling the actual generate_key test */
+    ASSERT_ALLOC_WEAK(buffer, key_bytes);
+    mbedtls_free( buffer );
+
+    test_generate_key( type_arg, bits_arg, usage_arg, alg_arg, expected_status_arg );
+exit:
+    return;
+}
+/* END_CASE */
+
 /* BEGIN_CASE depends_on:MBEDTLS_RSA_C:MBEDTLS_GENPRIME:MBEDTLS_PKCS1_V15 */
 void generate_key_rsa( int bits_arg,
                        data_t *e_arg,