diff --git a/test/quicapitest.c b/test/quicapitest.c
index 8d2b871b91..227f6de8c8 100644
--- a/test/quicapitest.c
+++ b/test/quicapitest.c
@@ -496,21 +496,15 @@ static int compare_with_file(BIO *membio)
  */
 static int test_ssl_trace(void)
 {
-    SSL_CTX *cctx = SSL_CTX_new_ex(libctx, NULL, OSSL_QUIC_client_method());
+    SSL_CTX *cctx = NULL;
     SSL *clientquic = NULL;
     QUIC_TSERVER *qtserv = NULL;
     int testresult = 0;
-    BIO *bio = BIO_new(BIO_s_mem());
+    BIO *bio = NULL;
 
-    /*
-     * Ensure we only configure ciphersuites that are available with both the
-     * default and fips providers to get the same output in both cases
-     */
-    if (!TEST_true(SSL_CTX_set_ciphersuites(cctx, "TLS_AES_128_GCM_SHA256")))
-        goto err;
-
-    if (!TEST_ptr(cctx)
-            || !TEST_ptr(bio)
+    if (!TEST_ptr(cctx = SSL_CTX_new_ex(libctx, NULL, OSSL_QUIC_client_method()))
+            || !TEST_ptr(bio = BIO_new(BIO_s_mem()))
+            || !TEST_true(SSL_CTX_set_ciphersuites(cctx, "TLS_AES_128_GCM_SHA256"))
             || !TEST_true(qtest_create_quic_objects(libctx, cctx, NULL, cert,
                                                     privkey,
                                                     QTEST_FLAG_FAKE_TIME,
@@ -524,8 +518,15 @@ static int test_ssl_trace(void)
     if (!TEST_true(qtest_create_quic_connection(qtserv, clientquic)))
         goto err;
 
-    if (!TEST_true(compare_with_file(bio)))
-        goto err;
+    /* Skip the comparison of the trace when the fips provider is used. */
+    if (is_fips) {
+        /* Check whether there was something written. */
+        if (!TEST_int_gt(BIO_pending(bio), 0))
+            goto err;
+    } else {
+        if (!TEST_true(compare_with_file(bio)))
+            goto err;
+    }
 
     testresult = 1;
  err:
diff --git a/test/ssl-tests/14-curves.cnf.in b/test/ssl-tests/14-curves.cnf.in
index 09b01e4acb..e6c048e8dd 100644
--- a/test/ssl-tests/14-curves.cnf.in
+++ b/test/ssl-tests/14-curves.cnf.in
@@ -12,8 +12,12 @@ use OpenSSL::Test::Utils qw(anydisabled);
 
 our $fips_mode;
 
-my @curves = ("prime256v1", "secp384r1", "secp521r1", "X25519",
-              "X448");
+my @curves = ("prime256v1", "secp384r1", "secp521r1");
+
+my @curves_no_fips = ("X25519", "X448");
+
+push @curves, @curves_no_fips if !$fips_mode;
+
 #Curves *only* suitable for use in TLSv1.3
 my @curves_tls_1_3 = ("ffdhe2048", "ffdhe3072", "ffdhe4096", "ffdhe6144",
                       "ffdhe8192");
diff --git a/test/ssl-tests/20-cert-select.cnf b/test/ssl-tests/20-cert-select.cnf
index 51d38b9b61..546b9ce091 100644
--- a/test/ssl-tests/20-cert-select.cnf
+++ b/test/ssl-tests/20-cert-select.cnf
@@ -19,12 +19,12 @@ test-13 = 13-Suite B P-256 Hash Algorithm Selection
 test-14 = 14-Suite B P-384 Hash Algorithm Selection
 test-15 = 15-Ed25519 CipherString and Signature Algorithm Selection
 test-16 = 16-Ed448 CipherString and Signature Algorithm Selection
-test-17 = 17-Ed25519 CipherString and Curves Selection
-test-18 = 18-Ed448 CipherString and Curves Selection
-test-19 = 19-TLS 1.2 Ed25519 Client Auth
-test-20 = 20-TLS 1.2 Ed448 Client Auth
-test-21 = 21-ECDSA Signature Algorithm Selection SHA1
-test-22 = 22-ECDSA with brainpool
+test-17 = 17-TLS 1.2 Ed25519 Client Auth
+test-18 = 18-TLS 1.2 Ed448 Client Auth
+test-19 = 19-ECDSA Signature Algorithm Selection SHA1
+test-20 = 20-ECDSA with brainpool
+test-21 = 21-Ed25519 CipherString and Curves Selection
+test-22 = 22-Ed448 CipherString and Curves Selection
 test-23 = 23-RSA-PSS Certificate CipherString Selection
 test-24 = 24-RSA-PSS Certificate Legacy Signature Algorithm Selection
 test-25 = 25-RSA-PSS Certificate Unified Signature Algorithm Selection
@@ -602,91 +602,21 @@ ExpectedServerSignType = Ed448
 
 # ===========================================================
 
-[17-Ed25519 CipherString and Curves Selection]
-ssl_conf = 17-Ed25519 CipherString and Curves Selection-ssl
+[17-TLS 1.2 Ed25519 Client Auth]
+ssl_conf = 17-TLS 1.2 Ed25519 Client Auth-ssl
 
-[17-Ed25519 CipherString and Curves Selection-ssl]
-server = 17-Ed25519 CipherString and Curves Selection-server
-client = 17-Ed25519 CipherString and Curves Selection-client
+[17-TLS 1.2 Ed25519 Client Auth-ssl]
+server = 17-TLS 1.2 Ed25519 Client Auth-server
+client = 17-TLS 1.2 Ed25519 Client Auth-client
 
-[17-Ed25519 CipherString and Curves Selection-server]
-Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
-CipherString = DEFAULT
-ECDSA.Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-cert.pem
-ECDSA.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ecdsa-key.pem
-Ed25519.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed25519-cert.pem
-Ed25519.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed25519-key.pem
-Ed448.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed448-cert.pem
-Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed448-key.pem
-MaxProtocol = TLSv1.2
-PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
-
-[17-Ed25519 CipherString and Curves Selection-client]
-CipherString = aECDSA
-Curves = X25519
-MaxProtocol = TLSv1.2
-SignatureAlgorithms = ECDSA+SHA256:ed25519
-VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
-VerifyMode = Peer
-
-[test-17]
-ExpectedResult = Success
-ExpectedServerCertType = Ed25519
-ExpectedServerSignType = Ed25519
-
-
-# ===========================================================
-
-[18-Ed448 CipherString and Curves Selection]
-ssl_conf = 18-Ed448 CipherString and Curves Selection-ssl
-
-[18-Ed448 CipherString and Curves Selection-ssl]
-server = 18-Ed448 CipherString and Curves Selection-server
-client = 18-Ed448 CipherString and Curves Selection-client
-
-[18-Ed448 CipherString and Curves Selection-server]
-Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
-CipherString = DEFAULT
-ECDSA.Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-cert.pem
-ECDSA.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ecdsa-key.pem
-Ed25519.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed25519-cert.pem
-Ed25519.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed25519-key.pem
-Ed448.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed448-cert.pem
-Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed448-key.pem
-MaxProtocol = TLSv1.2
-PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
-
-[18-Ed448 CipherString and Curves Selection-client]
-CipherString = aECDSA
-Curves = X448
-MaxProtocol = TLSv1.2
-SignatureAlgorithms = ECDSA+SHA256:ed448
-VerifyCAFile = ${ENV::TEST_CERTS_DIR}/root-ed448-cert.pem
-VerifyMode = Peer
-
-[test-18]
-ExpectedResult = Success
-ExpectedServerCertType = Ed448
-ExpectedServerSignType = Ed448
-
-
-# ===========================================================
-
-[19-TLS 1.2 Ed25519 Client Auth]
-ssl_conf = 19-TLS 1.2 Ed25519 Client Auth-ssl
-
-[19-TLS 1.2 Ed25519 Client Auth-ssl]
-server = 19-TLS 1.2 Ed25519 Client Auth-server
-client = 19-TLS 1.2 Ed25519 Client Auth-client
-
-[19-TLS 1.2 Ed25519 Client Auth-server]
+[17-TLS 1.2 Ed25519 Client Auth-server]
 Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
 CipherString = DEFAULT
 PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/root-cert.pem
 VerifyMode = Require
 
-[19-TLS 1.2 Ed25519 Client Auth-client]
+[17-TLS 1.2 Ed25519 Client Auth-client]
 CipherString = DEFAULT
 Ed25519.Certificate = ${ENV::TEST_CERTS_DIR}/client-ed25519-cert.pem
 Ed25519.PrivateKey = ${ENV::TEST_CERTS_DIR}/client-ed25519-key.pem
@@ -695,7 +625,7 @@ MinProtocol = TLSv1.2
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
 VerifyMode = Peer
 
-[test-19]
+[test-17]
 ExpectedClientCertType = Ed25519
 ExpectedClientSignType = Ed25519
 ExpectedResult = Success
@@ -703,21 +633,21 @@ ExpectedResult = Success
 
 # ===========================================================
 
-[20-TLS 1.2 Ed448 Client Auth]
-ssl_conf = 20-TLS 1.2 Ed448 Client Auth-ssl
+[18-TLS 1.2 Ed448 Client Auth]
+ssl_conf = 18-TLS 1.2 Ed448 Client Auth-ssl
 
-[20-TLS 1.2 Ed448 Client Auth-ssl]
-server = 20-TLS 1.2 Ed448 Client Auth-server
-client = 20-TLS 1.2 Ed448 Client Auth-client
+[18-TLS 1.2 Ed448 Client Auth-ssl]
+server = 18-TLS 1.2 Ed448 Client Auth-server
+client = 18-TLS 1.2 Ed448 Client Auth-client
 
-[20-TLS 1.2 Ed448 Client Auth-server]
+[18-TLS 1.2 Ed448 Client Auth-server]
 Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
 CipherString = DEFAULT
 PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/root-cert.pem
 VerifyMode = Require
 
-[20-TLS 1.2 Ed448 Client Auth-client]
+[18-TLS 1.2 Ed448 Client Auth-client]
 CipherString = DEFAULT
 Ed448.Certificate = ${ENV::TEST_CERTS_DIR}/client-ed448-cert.pem
 Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/client-ed448-key.pem
@@ -726,7 +656,7 @@ MinProtocol = TLSv1.2
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
 VerifyMode = Peer
 
-[test-20]
+[test-18]
 ExpectedClientCertType = Ed448
 ExpectedClientSignType = Ed448
 ExpectedResult = Success
@@ -734,14 +664,14 @@ ExpectedResult = Success
 
 # ===========================================================
 
-[21-ECDSA Signature Algorithm Selection SHA1]
-ssl_conf = 21-ECDSA Signature Algorithm Selection SHA1-ssl
+[19-ECDSA Signature Algorithm Selection SHA1]
+ssl_conf = 19-ECDSA Signature Algorithm Selection SHA1-ssl
 
-[21-ECDSA Signature Algorithm Selection SHA1-ssl]
-server = 21-ECDSA Signature Algorithm Selection SHA1-server
-client = 21-ECDSA Signature Algorithm Selection SHA1-client
+[19-ECDSA Signature Algorithm Selection SHA1-ssl]
+server = 19-ECDSA Signature Algorithm Selection SHA1-server
+client = 19-ECDSA Signature Algorithm Selection SHA1-client
 
-[21-ECDSA Signature Algorithm Selection SHA1-server]
+[19-ECDSA Signature Algorithm Selection SHA1-server]
 Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
 CipherString = DEFAULT:@SECLEVEL=0
 ECDSA.Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-cert.pem
@@ -753,13 +683,13 @@ Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed448-key.pem
 MaxProtocol = TLSv1.2
 PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
 
-[21-ECDSA Signature Algorithm Selection SHA1-client]
+[19-ECDSA Signature Algorithm Selection SHA1-client]
 CipherString = DEFAULT:@SECLEVEL=0
 SignatureAlgorithms = ECDSA+SHA1
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
 VerifyMode = Peer
 
-[test-21]
+[test-19]
 ExpectedResult = Success
 ExpectedServerCertType = P-256
 ExpectedServerSignHash = SHA1
@@ -768,20 +698,20 @@ ExpectedServerSignType = EC
 
 # ===========================================================
 
-[22-ECDSA with brainpool]
-ssl_conf = 22-ECDSA with brainpool-ssl
+[20-ECDSA with brainpool]
+ssl_conf = 20-ECDSA with brainpool-ssl
 
-[22-ECDSA with brainpool-ssl]
-server = 22-ECDSA with brainpool-server
-client = 22-ECDSA with brainpool-client
+[20-ECDSA with brainpool-ssl]
+server = 20-ECDSA with brainpool-server
+client = 20-ECDSA with brainpool-client
 
-[22-ECDSA with brainpool-server]
+[20-ECDSA with brainpool-server]
 Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-brainpoolP256r1-cert.pem
 CipherString = DEFAULT
 Groups = brainpoolP256r1
 PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ecdsa-brainpoolP256r1-key.pem
 
-[22-ECDSA with brainpool-client]
+[20-ECDSA with brainpool-client]
 CipherString = aECDSA
 Groups = brainpoolP256r1
 MaxProtocol = TLSv1.2
@@ -789,13 +719,83 @@ RequestCAFile = ${ENV::TEST_CERTS_DIR}/root-cert.pem
 VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
 VerifyMode = Peer
 
-[test-22]
+[test-20]
 ExpectedResult = Success
 ExpectedServerCANames = empty
 ExpectedServerCertType = brainpoolP256r1
 ExpectedServerSignType = EC
 
 
+# ===========================================================
+
+[21-Ed25519 CipherString and Curves Selection]
+ssl_conf = 21-Ed25519 CipherString and Curves Selection-ssl
+
+[21-Ed25519 CipherString and Curves Selection-ssl]
+server = 21-Ed25519 CipherString and Curves Selection-server
+client = 21-Ed25519 CipherString and Curves Selection-client
+
+[21-Ed25519 CipherString and Curves Selection-server]
+Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
+CipherString = DEFAULT
+ECDSA.Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-cert.pem
+ECDSA.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ecdsa-key.pem
+Ed25519.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed25519-cert.pem
+Ed25519.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed25519-key.pem
+Ed448.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed448-cert.pem
+Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed448-key.pem
+MaxProtocol = TLSv1.2
+PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
+
+[21-Ed25519 CipherString and Curves Selection-client]
+CipherString = aECDSA
+Curves = X25519
+MaxProtocol = TLSv1.2
+SignatureAlgorithms = ECDSA+SHA256:ed25519
+VerifyCAFile = ${ENV::TEST_CERTS_DIR}/rootcert.pem
+VerifyMode = Peer
+
+[test-21]
+ExpectedResult = Success
+ExpectedServerCertType = Ed25519
+ExpectedServerSignType = Ed25519
+
+
+# ===========================================================
+
+[22-Ed448 CipherString and Curves Selection]
+ssl_conf = 22-Ed448 CipherString and Curves Selection-ssl
+
+[22-Ed448 CipherString and Curves Selection-ssl]
+server = 22-Ed448 CipherString and Curves Selection-server
+client = 22-Ed448 CipherString and Curves Selection-client
+
+[22-Ed448 CipherString and Curves Selection-server]
+Certificate = ${ENV::TEST_CERTS_DIR}/servercert.pem
+CipherString = DEFAULT
+ECDSA.Certificate = ${ENV::TEST_CERTS_DIR}/server-ecdsa-cert.pem
+ECDSA.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ecdsa-key.pem
+Ed25519.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed25519-cert.pem
+Ed25519.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed25519-key.pem
+Ed448.Certificate = ${ENV::TEST_CERTS_DIR}/server-ed448-cert.pem
+Ed448.PrivateKey = ${ENV::TEST_CERTS_DIR}/server-ed448-key.pem
+MaxProtocol = TLSv1.2
+PrivateKey = ${ENV::TEST_CERTS_DIR}/serverkey.pem
+
+[22-Ed448 CipherString and Curves Selection-client]
+CipherString = aECDSA
+Curves = X448
+MaxProtocol = TLSv1.2
+SignatureAlgorithms = ECDSA+SHA256:ed448
+VerifyCAFile = ${ENV::TEST_CERTS_DIR}/root-ed448-cert.pem
+VerifyMode = Peer
+
+[test-22]
+ExpectedResult = Success
+ExpectedServerCertType = Ed448
+ExpectedServerSignType = Ed448
+
+
 # ===========================================================
 
 [23-RSA-PSS Certificate CipherString Selection]
diff --git a/test/ssl-tests/20-cert-select.cnf.in b/test/ssl-tests/20-cert-select.cnf.in
index b8e689d565..6c9db7a907 100644
--- a/test/ssl-tests/20-cert-select.cnf.in
+++ b/test/ssl-tests/20-cert-select.cnf.in
@@ -328,41 +328,6 @@ our @tests = (
             "ExpectedResult" => "Success"
         },
     },
-    {
-        name => "Ed25519 CipherString and Curves Selection",
-        server => $server,
-        client => {
-            "CipherString" => "aECDSA",
-            "MaxProtocol" => "TLSv1.2",
-            "SignatureAlgorithms" => "ECDSA+SHA256:ed25519",
-            # Excluding P-256 from the supported curves list means server
-            # certificate should be Ed25519 and not P-256
-            "Curves" => "X25519"
-        },
-        test   => {
-            "ExpectedServerCertType" =>, "Ed25519",
-            "ExpectedServerSignType" =>, "Ed25519",
-            "ExpectedResult" => "Success"
-        },
-    },
-    {
-        name => "Ed448 CipherString and Curves Selection",
-        server => $server,
-        client => {
-            "CipherString" => "aECDSA",
-            "MaxProtocol" => "TLSv1.2",
-            "SignatureAlgorithms" => "ECDSA+SHA256:ed448",
-            "VerifyCAFile" => test_pem("root-ed448-cert.pem"),
-            # Excluding P-256 from the supported curves list means server
-            # certificate should be Ed25519 and not P-256
-            "Curves" => "X448"
-        },
-        test   => {
-            "ExpectedServerCertType" =>, "Ed448",
-            "ExpectedServerSignType" =>, "Ed448",
-            "ExpectedResult" => "Success"
-        },
-    },
     {
         name => "TLS 1.2 Ed25519 Client Auth",
         server => {
@@ -446,6 +411,41 @@ my @tests_non_fips = (
             "ExpectedResult" => "Success"
         },
     },
+    {
+        name => "Ed25519 CipherString and Curves Selection",
+        server => $server,
+        client => {
+            "CipherString" => "aECDSA",
+            "MaxProtocol" => "TLSv1.2",
+            "SignatureAlgorithms" => "ECDSA+SHA256:ed25519",
+            # Excluding P-256 from the supported curves list means server
+            # certificate should be Ed25519 and not P-256
+            "Curves" => "X25519"
+        },
+        test   => {
+            "ExpectedServerCertType" =>, "Ed25519",
+            "ExpectedServerSignType" =>, "Ed25519",
+            "ExpectedResult" => "Success"
+        },
+    },
+    {
+        name => "Ed448 CipherString and Curves Selection",
+        server => $server,
+        client => {
+            "CipherString" => "aECDSA",
+            "MaxProtocol" => "TLSv1.2",
+            "SignatureAlgorithms" => "ECDSA+SHA256:ed448",
+            "VerifyCAFile" => test_pem("root-ed448-cert.pem"),
+            # Excluding P-256 from the supported curves list means server
+            # certificate should be Ed25519 and not P-256
+            "Curves" => "X448"
+        },
+        test   => {
+            "ExpectedServerCertType" =>, "Ed448",
+            "ExpectedServerSignType" =>, "Ed448",
+            "ExpectedResult" => "Success"
+        },
+    },
 );
 
 my @tests_pss = (
diff --git a/test/ssl-tests/28-seclevel.cnf.in b/test/ssl-tests/28-seclevel.cnf.in
index 9204f215e5..789817cc9a 100644
--- a/test/ssl-tests/28-seclevel.cnf.in
+++ b/test/ssl-tests/28-seclevel.cnf.in
@@ -56,7 +56,10 @@ our @tests_ec = (
         client => { "CipherString" => "DEFAULT:\@SECLEVEL=5",
                     "VerifyCAFile" => test_pem("root-ed448-cert.pem") },
         test   => { "ExpectedResult" => "ServerFail" },
-    },
+    }
+);
+
+our @tests_ec_non_fips = (
     {
         name => "SECLEVEL 3 with P-384 key, X25519 ECDHE",
         server => { "CipherString" => "DEFAULT:\@SECLEVEL=3",
@@ -81,5 +84,6 @@ our @tests_tls1_2 = (
     },
 );
 
+push @tests_ec, @tests_ec_non_fips unless $fips_mode;
 push @tests, @tests_ec unless disabled("ecx");
 push @tests, @tests_tls1_2 unless disabled("tls1_2") || disabled("ecx");