diff --git a/tests/opt-testcases/tls13-misc.sh b/tests/opt-testcases/tls13-misc.sh
index cc650c1..8b9d575 100755
--- a/tests/opt-testcases/tls13-misc.sh
+++ b/tests/opt-testcases/tls13-misc.sh
@@ -287,8 +287,9 @@
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_all_configs_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
-                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
                              MBEDTLS_SSL_EARLY_DATA
+requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED
 run_test    "TLS 1.3 m->G: EarlyData: basic check, good" \
             "$G_NEXT_SRV -d 10 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:+ECDHE-PSK:+PSK --earlydata --disable-client-cert" \
             "$P_CLI debug_level=4 force_version=tls13 early_data=1 reco_mode=1 reconnect=1 reco_delay=2" \
@@ -307,8 +308,9 @@
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_all_configs_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
-                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
                              MBEDTLS_SSL_EARLY_DATA
+requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED
 run_test    "TLS 1.3 m->G: EarlyData: hybrid check, good" \
             "$G_NEXT_SRV -d 10 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:+ECDHE-PSK:+PSK --earlydata --disable-client-cert" \
             "$P_CLI debug_level=4 early_data=1 reco_mode=1 reconnect=1 reco_delay=2" \
@@ -327,9 +329,10 @@
 requires_config_enabled MBEDTLS_SSL_CLI_C
 requires_all_configs_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
-                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
                              MBEDTLS_SSL_EARLY_DATA
-run_test    "TLS 1.3 m->G: EarlyData: negative check, fail" \
+requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED
+run_test    "TLS 1.3 m->G: EarlyData: no early_data in NewSessionTicket, good." \
             "$G_NEXT_SRV -d 10 --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+CIPHER-ALL:+ECDHE-PSK:+PSK --disable-client-cert" \
             "$P_CLI debug_level=4 early_data=1 reco_mode=1 reconnect=1 reco_delay=2" \
             0 \
@@ -339,11 +342,16 @@
             -C "EncryptedExtensions: early_data(42) extension received." \
             -C "EncryptedExtensions: early_data(42) extension ( ignored )."
 
-#TODO openssl compatible mode can't work currently, it will need external psk.
+#TODO: OpenSSL tests don't work now. It might be openssl options issue, cause GnuTLS has worked.
 skip_next_test
-requires_config_enabled MBEDTLS_SSL_SRV_C
+requires_openssl_tls1_3
+requires_config_enabled MBEDTLS_DEBUG_C
 requires_config_enabled MBEDTLS_SSL_CLI_C
-requires_config_enabled MBEDTLS_SSL_EARLY_DATA
+requires_all_configs_enabled MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_EARLY_DATA
+requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED
 run_test    "TLS 1.3, ext PSK, early data" \
             "$O_NEXT_SRV_EARLY_DATA -msg -debug -tls1_3 -psk_identity 0a0b0c -psk 010203 -allow_no_dhe_kex -nocert" \
             "$P_CLI debug_level=5 force_version=tls13 tls13_kex_modes=psk early_data=1 psk=010203 psk_identity=0a0b0c" \
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index 4b6a4cb..245324a 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -2105,7 +2105,6 @@
     scripts/config.py unset MBEDTLS_HKDF_C # has independent PSA implementation
     scripts/config.py unset MBEDTLS_HMAC_DRBG_C
     scripts/config.py unset MBEDTLS_ECDSA_DETERMINISTIC
-    scripts/config.py unset MBEDTLS_SSL_EARLY_DATA
     scripts/config.py -f include/psa/crypto_config.h unset PSA_WANT_ALG_DETERMINISTIC_ECDSA
 
     loc_accel_flags="$loc_accel_flags $( echo "$loc_accel_list" | sed 's/[^ ]* */-DMBEDTLS_PSA_ACCEL_&/g' )"