diff --git a/test/ciphername_test.c b/test/ciphername_test.c
index c4ec6cadd740bb..8f10f26ba1687a 100644
--- a/test/ciphername_test.c
+++ b/test/ciphername_test.c
@@ -361,6 +361,8 @@ static CIPHER_ID_NAME cipher_names[] = {
     {0x1303, "TLS_CHACHA20_POLY1305_SHA256"},
     {0x1304, "TLS_AES_128_CCM_SHA256"},
     {0x1305, "TLS_AES_128_CCM_8_SHA256"},
+    {0xC0B4, "TLS_SHA256_SHA256"},
+    {0xC0B5, "TLS_SHA384_SHA384"},
     {0xFEFE, "SSL_RSA_FIPS_WITH_DES_CBC_SHA"},
     {0xFEFF, "SSL_RSA_FIPS_WITH_3DES_EDE_CBC_SHA"},
 };
diff --git a/test/evp_libctx_test.c b/test/evp_libctx_test.c
index 2448c35a149f60..9290a2d7a4583a 100644
--- a/test/evp_libctx_test.c
+++ b/test/evp_libctx_test.c
@@ -334,7 +334,11 @@ static int test_cipher_reinit(int test_id)
         0x03, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
         0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
     };
-    unsigned char iv[16] = {
+    unsigned char iv[48] = {
+        0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
+        0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00,
+        0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
+        0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00,
         0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
         0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00
     };
@@ -425,7 +429,11 @@ static int test_cipher_reinit_partialupdate(int test_id)
         0x03, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
         0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
     };
-    static const unsigned char iv[16] = {
+    static const unsigned char iv[48] = {
+        0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
+        0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00,
+        0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
+        0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00,
         0x0f, 0x0e, 0x0d, 0x0c, 0x0b, 0x0a, 0x09, 0x08,
         0x07, 0x06, 0x05, 0x04, 0x03, 0x02, 0x01, 0x00
     };
diff --git a/test/helpers/ssltestlib.h b/test/helpers/ssltestlib.h
index 871f9bd52e09db..468662ed0bfd7a 100644
--- a/test/helpers/ssltestlib.h
+++ b/test/helpers/ssltestlib.h
@@ -17,6 +17,8 @@
 #define TLS13_CHACHA20_POLY1305_SHA256_BYTES ((const unsigned char *)"\x13\x03")
 #define TLS13_AES_128_CCM_SHA256_BYTES ((const unsigned char *)"\x13\x04")
 #define TLS13_AES_128_CCM_8_SHA256_BYTES ((const unsigned char *)"\x13\05")
+#define TLS13_SHA256_SHA256_BYTES ((const unsigned char *)"\xC0\xB4")
+#define TLS13_SHA384_SHA384_BYTES ((const unsigned char *)"\xC0\xB5")
 
 int create_ssl_ctx_pair(OSSL_LIB_CTX *libctx, const SSL_METHOD *sm,
                         const SSL_METHOD *cm, int min_proto_version,
diff --git a/test/quicapitest.c b/test/quicapitest.c
index 41cf0fc7a87ead..ea7249b2a4fece 100644
--- a/test/quicapitest.c
+++ b/test/quicapitest.c
@@ -336,7 +336,11 @@ static int test_cipher_find(void)
         { TLS13_AES_256_GCM_SHA384_BYTES, 1 },
         { TLS13_CHACHA20_POLY1305_SHA256_BYTES, 1 },
         { TLS13_AES_128_CCM_SHA256_BYTES, 0 },
-        { TLS13_AES_128_CCM_8_SHA256_BYTES, 0 }
+        { TLS13_AES_128_CCM_8_SHA256_BYTES, 0 },
+#if !defined(OPENSSL_NO_INTEGRITY_ONLY_CIPHER)
+        { TLS13_SHA256_SHA256_BYTES, 0 },
+        { TLS13_SHA384_SHA384_BYTES, 0 }
+#endif
     };
     size_t i;
     int testresult = 0;
@@ -581,7 +585,9 @@ static int test_quic_forbidden_apis_ctx(void)
 #define NON_QUIC_CIPHERSUITES           \
     "TLS_AES_128_CCM_SHA256:"           \
     "TLS_AES_256_CCM_SHA384:"           \
-    "TLS_AES_128_CCM_8_SHA256"
+    "TLS_AES_128_CCM_8_SHA256:"         \
+    "TLS_SHA256_SHA256:"                \
+    "TLS_SHA384_SHA384"                 \
 
     /* Set TLSv1.3 ciphersuite list for the SSL_CTX. */
     if (!TEST_true(SSL_CTX_set_ciphersuites(ctx,
diff --git a/test/sslapitest.c b/test/sslapitest.c
index efea1a6495444e..b38c5dcbc6aa66 100644
--- a/test/sslapitest.c
+++ b/test/sslapitest.c
@@ -3841,7 +3841,11 @@ static const char *ciphersuites[] = {
     "TLS_AES_256_GCM_SHA384",
     "TLS_AES_128_CCM_SHA256",
 #if !defined(OPENSSL_NO_CHACHA) && !defined(OPENSSL_NO_POLY1305)
-    "TLS_CHACHA20_POLY1305_SHA256"
+    "TLS_CHACHA20_POLY1305_SHA256",
+#endif
+#if !defined(OPENSSL_NO_INTEGRITY_ONLY_CIPHER)
+    "TLS_SHA256_SHA256",
+    "TLS_SHA384_SHA384"
 #endif
 };
 
@@ -3862,7 +3866,7 @@ static int early_data_skip_helper(int testtype, int cipher, int idx)
     unsigned char buf[20];
     size_t readbytes, written;
 
-    if (is_fips && cipher == 4)
+    if (is_fips && (cipher == 4 || cipher == 5 || cipher == 6))
         return 1;
 
     if (!TEST_true(create_ssl_ctx_pair(libctx, TLS_server_method(),
@@ -3871,7 +3875,7 @@ static int early_data_skip_helper(int testtype, int cipher, int idx)
                                               &sctx, &cctx, cert, privkey)))
         goto end;
 
-    if (cipher == 0) {
+    if (cipher == 0 || cipher == 5 || cipher == 6) {
         SSL_CTX_set_security_level(sctx, 0);
         SSL_CTX_set_security_level(cctx, 0);
     }
@@ -3882,8 +3886,9 @@ static int early_data_skip_helper(int testtype, int cipher, int idx)
 
     if (!TEST_true(setupearly_data_test(&cctx, &sctx, &clientssl,
                                         &serverssl, &sess, idx,
-                                        cipher == 2 ? SHA384_DIGEST_LENGTH
-                                                    : SHA256_DIGEST_LENGTH)))
+                                        cipher == 2 || cipher == 6
+                                            ? SHA384_DIGEST_LENGTH
+                                            : SHA256_DIGEST_LENGTH)))
         goto end;
 
     if (testtype == 1 || testtype == 2) {
@@ -4334,12 +4339,14 @@ static int test_early_data_psk(int idx)
 }
 
 /*
- * Test TLSv1.3 PSK can be used to send early_data with all 5 ciphersuites
+ * Test TLSv1.3 PSK can be used to send early_data with all 7 ciphersuites
  * idx == 0: Test with TLS1_3_RFC_AES_128_GCM_SHA256
  * idx == 1: Test with TLS1_3_RFC_AES_256_GCM_SHA384
  * idx == 2: Test with TLS1_3_RFC_CHACHA20_POLY1305_SHA256,
  * idx == 3: Test with TLS1_3_RFC_AES_128_CCM_SHA256
  * idx == 4: Test with TLS1_3_RFC_AES_128_CCM_8_SHA256
+ * idx == 5: Test with TLS1_3_RFC_SHA256_SHA256
+ * idx == 6: Test with TLS1_3_RFC_SHA384_SHA384
  */
 static int test_early_data_psk_with_all_ciphers(int idx)
 {
@@ -4359,7 +4366,14 @@ static int test_early_data_psk_with_all_ciphers(int idx)
         NULL,
 # endif
         TLS1_3_RFC_AES_128_CCM_SHA256,
-        TLS1_3_RFC_AES_128_CCM_8_SHA256
+        TLS1_3_RFC_AES_128_CCM_8_SHA256,
+# if !defined(OPENSSL_NO_INTEGRITY_ONLY_CIPHER)
+        TLS1_3_RFC_SHA256_SHA256,
+        TLS1_3_RFC_SHA384_SHA384
+#else
+        NULL,
+        NULL
+#endif
     };
     const unsigned char *cipher_bytes[] = {
         TLS13_AES_128_GCM_SHA256_BYTES,
@@ -4370,13 +4384,23 @@ static int test_early_data_psk_with_all_ciphers(int idx)
         NULL,
 # endif
         TLS13_AES_128_CCM_SHA256_BYTES,
-        TLS13_AES_128_CCM_8_SHA256_BYTES
+        TLS13_AES_128_CCM_8_SHA256_BYTES,
+# if !defined(OPENSSL_NO_INTEGRITY_ONLY_CIPHER)
+        TLS13_SHA256_SHA256_BYTES,
+        TLS13_SHA384_SHA384_BYTES
+#else
+        NULL,
+        NULL
+#endif
     };
 
     if (cipher_str[idx] == NULL)
         return 1;
-    /* Skip ChaCha20Poly1305 as currently FIPS module does not support it */
-    if (idx == 2 && is_fips == 1)
+    /*
+     * Skip ChaCha20Poly1305 & TLS_SHA{256,384}_SHA{256,384} cipher as
+     * currently FIPS module does not support it.
+     */
+    if ((idx == 2 || idx == 5 || idx == 6) && is_fips == 1)
         return 1;
 
     /* We always set this up with a final parameter of "2" for PSK */
@@ -4385,7 +4409,7 @@ static int test_early_data_psk_with_all_ciphers(int idx)
                                         SHA384_DIGEST_LENGTH)))
         goto end;
 
-    if (idx == 4) {
+    if (idx == 4 || idx == 5 || idx == 6) {
         /* CCM8 ciphers are considered low security due to their short tag */
         SSL_set_security_level(clientssl, 0);
         SSL_set_security_level(serverssl, 0);
@@ -5232,7 +5256,12 @@ static int test_tls13_ciphersuite(int idx)
 # endif
         /* CCM8 ciphers are considered low security due to their short tag */
         { TLS1_3_RFC_AES_128_CCM_8_SHA256
-          ":" TLS1_3_RFC_AES_128_CCM_SHA256, 1, 1 }
+          ":" TLS1_3_RFC_AES_128_CCM_SHA256, 1, 1 },
+# if !defined(OPENSSL_NO_INTEGRITY_ONLY_CIPHER)
+        /* Integrity-only cipher do not provide any confidentiality */
+        { TLS1_3_RFC_SHA256_SHA256
+          ":" TLS1_3_RFC_SHA384_SHA384, 0, 1 }
+# endif
     };
     const char *t13_cipher = NULL;
     const char *t12_cipher = NULL;
@@ -11552,7 +11581,7 @@ int setup_tests(void)
     ADD_ALL_TESTS(test_early_data_skip_abort, OSSL_NELEM(ciphersuites) * 3);
     ADD_ALL_TESTS(test_early_data_not_sent, 3);
     ADD_ALL_TESTS(test_early_data_psk, 8);
-    ADD_ALL_TESTS(test_early_data_psk_with_all_ciphers, 5);
+    ADD_ALL_TESTS(test_early_data_psk_with_all_ciphers, 7);
     ADD_ALL_TESTS(test_early_data_not_expected, 3);
 # ifndef OPENSSL_NO_TLS1_2
     ADD_ALL_TESTS(test_early_data_tls1_2, 3);