diff --git a/library/pk.c b/library/pk.c
index 7bc1da8..1d85c92 100644
--- a/library/pk.c
+++ b/library/pk.c
@@ -1444,7 +1444,8 @@
 
         if (PSA_ALG_IS_RSA_OAEP(alg_type) || PSA_ALG_IS_RSA_PSS(alg_type)) {
             ret = mbedtls_rsa_set_padding(mbedtls_pk_rsa(*pk), MBEDTLS_RSA_PKCS_V21, md_type);
-        } else {
+        } else if (PSA_ALG_IS_RSA_PKCS1V15_SIGN(alg_type) ||
+                   alg_type == PSA_ALG_RSA_PKCS1V15_CRYPT) {
             ret = mbedtls_rsa_set_padding(mbedtls_pk_rsa(*pk), MBEDTLS_RSA_PKCS_V15, md_type);
         }
         if (ret != 0) {
diff --git a/tests/suites/test_suite_pk.data b/tests/suites/test_suite_pk.data
index a1fe5db..561297c 100644
--- a/tests/suites/test_suite_pk.data
+++ b/tests/suites/test_suite_pk.data
@@ -1567,10 +1567,14 @@
 depends_on:MBEDTLS_RSA_C:MBEDTLS_PKCS1_V21:MBEDTLS_MD_CAN_SHA512
 pk_copy_from_psa_success:"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":PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_ALG_RSA_PSS(PSA_ALG_SHA_512)
 
-# Key's algorithm is wrong for an RSA key, but pk_copy_from_psa() ignores
-# this information when building the PK context.
+Copy from PSA: valid RSA, PSA_ALG_NONE
+depends_on:MBEDTLS_RSA_C:MBEDTLS_MD_ALG_FOR_TEST
+pk_copy_from_psa_success:"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":PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_ALG_NONE
+
+# Key's algorithm is wrong for an RSA key, but pk_copy_from_psa() accepts
+# it anyway.
 Copy from PSA: valid RSA, wrong alg (CMAC)
-depends_on:MBEDTLS_RSA_C:MBEDTLS_PKCS1_V15:MBEDTLS_MD_ALG_FOR_TEST
+depends_on:MBEDTLS_RSA_C:MBEDTLS_MD_ALG_FOR_TEST
 pk_copy_from_psa_success:"308204a40201000282010100ef24d80f6b7a0f62ab2f750a8370c1c39781abe2f7ae5cbc698ebbc51067af68c8b02e5bfafe0b296a2fdca8ee5327bf3370bd26c529d173c4356d8ad51f606ac730e3be509d8535c9c51927222d6c4e770efec4d9b0bd11410e5e2e01e093700d358aab8292297483c65870ea6d4ca9299f4347790f6223480732726a97b34bb4d53cb3f188e3c97115b029fa9a2cce4c6d935977a90737ac8b2a2c5691ad928b22681ca05ee38ddba2278c854f51281c5e4856090aca59bf719a167e63bb932580ae2b599e1a297194696e637a919bc9d2caf214e59d46ed1a12e591b608f2031744111551430d9ac39082957ae1ce03a88068896701e6ce19a83890ff5761020301000102820100706fb53a02c13fcc9749d7d09a9e002c12e6bfc715c6a00961e3defab74cd896fe8c7f2f75e1cda3aa2e58a400718e65822d0671dd0f5d4ffdb7550a8a4b974c7cdccaa72745f864a2ba0daa6d9247b2d89d6f41644c89883c3b2222a5754e3cc7a91dcaa7b84acf6249763998aeccf558016e638352ad44835006f2ee94e691d0070ce561677f2a22a12f357bd762c57f80f1f4921f0f26b3ed758478d11086c182874355ef5039e8d854291b9ce7f8b284ec81f141b7255313507f5ea159d6b1c0ee176e7743d3c65d536e1e4aaf24089c1e00c8021012b8846a4971a0695030504ace362077e8b2fcb4fbdd70bfb734a3fe7d9e1a25bdd0cb0f2fcb56ecc502818100f8fdfbac1c033911b5a184980d081f700f4d450cebf18cbdc68f160a5abd580e6f8f5800fd0b60521dbe2d549e82617afe70d2ad004c2f45405d94e4418e8c2b8da6bcaa407bbfa5477b5a6fceccfcb99f51c6c16bd17202d997bdcaec83b870e3e101acc05e0754020ec207ef5ec9934ac81cd617af72cd94b2bb400eb2078302818100f5dfe74a548c04950178f50130d5aadbe5d1f4b52527c0bfad9aa0d73731fb24219cb5ea5c4b4fa56133d5ea9225fa7d0ccc9bdcc78b77303a2e73c17e9a46b9b09020604496a849f069d0d87713e06a5d374271b2629f5ba220506b606a101828d20da9fcfa3a7e75b135987260be6d37622fc3f4bf4fd2dfd9655da5ff0c4b02818100d4d797c959f0cf59fa1f65ceec64e32ad189c5daf3ddf9e747d28c8eb15e65e5812bd19896b6a0d1d126fe6cf54a92b5a6c71ef04feed001acb1d253044f2c3716d14f396201e6a30c65bfbb0fd65ebaf61bdb80ffff7c2c3f80dcf69813491907531231700770d0392a1066e411ecd201fce9d98149b32355572b85e889faad028181009d898bc165709d52f7b18f91e6bf508d3ab08ed12df04da0c2d40b7039ce4d72b61299c082c8424cdd7dfff71f13346ec12fac42069cc68e6108f86427012485bfaa6904258e3e5fb9a9a305bf2e3e21087eea94bcce51fabd63650397affd85ed49c1358480b3cfe90ad5234b4dcf555d220d26c9ff765ecfcc94152fd1be070281804bf77b4bae8386772de830cc75f2d1d4b8221b3f817208e08c002ac0549902677e4f0e7bce5ba1b3da74fbbe138758e6853b4a5b7bf0672bc1170c64fa502a5e24e3472db433b4e30761eab6ebb9e207235fd88b97b1b30e14f364b628219d6e17056543a4e29a4de1e41ad37927ce23d0442623744bc35a1874296960029044":PSA_KEY_TYPE_RSA_KEY_PAIR:PSA_ALG_CMAC
 
 Copy from PSA: non-exportable -> public, RSA
diff --git a/tests/suites/test_suite_pk.function b/tests/suites/test_suite_pk.function
index 81d6dd5..2feb9c4 100644
--- a/tests/suites/test_suite_pk.function
+++ b/tests/suites/test_suite_pk.function
@@ -2547,14 +2547,36 @@
      * - Verify with the PK context generated using public key.
      * - Verify using the public PSA key directly.
      */
-    TEST_EQUAL(mbedtls_pk_sign(&pk_priv, md_for_test, in_buf, in_buf_len,
-                               out_buf, sizeof(out_buf), &out_buf_len,
-                               mbedtls_test_rnd_std_rand, NULL), 0);
 
-    TEST_EQUAL(mbedtls_pk_verify(&pk_priv, md_for_test, in_buf, in_buf_len,
-                                 out_buf, out_buf_len), 0);
-    TEST_EQUAL(mbedtls_pk_verify(&pk_pub, md_for_test, in_buf, in_buf_len,
-                                 out_buf, out_buf_len), 0);
+    /* Edge cases: in a build with RSA key support but not RSA padding modes,
+     * or with ECDSA verify support but not signature, the signature might be
+     * impossible. */
+    int pk_can_sign = 0;
+#if defined(MBEDTLS_PKCS1_V15)
+    if (PSA_ALG_IS_RSA_PKCS1V15_SIGN(key_alg) || key_alg == PSA_ALG_RSA_PKCS1V15_CRYPT) {
+        pk_can_sign = 1;
+    }
+#endif
+#if defined(MBEDTLS_PKCS1_V21)
+    if (PSA_ALG_IS_RSA_PSS(key_alg) || PSA_ALG_IS_RSA_OAEP(key_alg)) {
+        pk_can_sign = 1;
+    }
+#endif
+#if defined(MBEDTLS_PK_CAN_ECDSA_SIGN)
+    if (PSA_ALG_IS_ECDSA(key_alg) || PSA_ALG_IS_DETERMINISTIC_ECDSA(key_alg)) {
+        pk_can_sign = 1;
+    }
+#endif
+    if (pk_can_sign) {
+        TEST_EQUAL(mbedtls_pk_sign(&pk_priv, md_for_test, in_buf, in_buf_len,
+                                   out_buf, sizeof(out_buf), &out_buf_len,
+                                   mbedtls_test_rnd_std_rand, NULL), 0);
+
+        TEST_EQUAL(mbedtls_pk_verify(&pk_priv, md_for_test, in_buf, in_buf_len,
+                                     out_buf, out_buf_len), 0);
+        TEST_EQUAL(mbedtls_pk_verify(&pk_pub, md_for_test, in_buf, in_buf_len,
+                                     out_buf, out_buf_len), 0);
+    }
 
     if (PSA_ALG_IS_HASH_AND_SIGN(key_alg)) {
 #if defined(MBEDTLS_PSA_UTIL_HAVE_ECDSA)