diff --git a/library/ssl_tls13_server.c b/library/ssl_tls13_server.c
index cc8a0a1..44abb4b 100644
--- a/library/ssl_tls13_server.c
+++ b/library/ssl_tls13_server.c
@@ -1767,31 +1767,24 @@
 
     if (ssl->conf->early_data_enabled == MBEDTLS_SSL_EARLY_DATA_DISABLED) {
         MBEDTLS_SSL_DEBUG_MSG(
-            1, ("EarlyData: rejected. configured disabled."));
-        return;
-    }
-
-    MBEDTLS_SSL_DEBUG_MSG(
-        3, ("EarlyData: conf->max_early_data_size = %u",
-            (unsigned int) ssl->conf->max_early_data_size));
-
-    if (!mbedtls_ssl_conf_tls13_some_psk_enabled(ssl)) {
-        MBEDTLS_SSL_DEBUG_MSG(
             1,
-            ("EarlyData: rejected. psk or psk_ephemeral is not available."));
+            ("EarlyData: rejected, feature disabled in server configuration."));
         return;
     }
 
-    if (handshake && handshake->resume != 1) {
+    if (!handshake->resume) {
+        /* We currently support early data only in the case of PSKs established
+           via a NewSessionTicket message thus in the case of a session
+           resumption. */
         MBEDTLS_SSL_DEBUG_MSG(
-            1, ("EarlyData: rejected. not resumption session."));
+            1, ("EarlyData: rejected, not resumption session."));
         return;
     }
 
     if (session->tls_version != MBEDTLS_SSL_VERSION_TLS1_3) {
         MBEDTLS_SSL_DEBUG_MSG(
             1,
-            ("EarlyData: rejected. not a TLS 1.3 ticket."));
+            ("EarlyData: rejected, not a TLS 1.3 ticket."));
         return;
     }
 
diff --git a/tests/opt-testcases/tls13-misc.sh b/tests/opt-testcases/tls13-misc.sh
index dbc2e43..ffa914e 100755
--- a/tests/opt-testcases/tls13-misc.sh
+++ b/tests/opt-testcases/tls13-misc.sh
@@ -500,7 +500,7 @@
 requires_all_configs_enabled MBEDTLS_SSL_EARLY_DATA MBEDTLS_SSL_SESSION_TICKETS     \
                              MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C MBEDTLS_HAVE_TIME    \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
-                             MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_ECP_LIGHT
+                             MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
 run_test "TLS 1.3 G->m: EarlyData: feature is disabled, fail." \
@@ -513,17 +513,19 @@
          -s "Last error was: -29056 - SSL - Verification of the message MAC failed"
 
 requires_gnutls_next
+
 requires_all_configs_enabled MBEDTLS_SSL_EARLY_DATA MBEDTLS_SSL_SESSION_TICKETS \
                              MBEDTLS_SSL_SRV_C MBEDTLS_DEBUG_C MBEDTLS_HAVE_TIME \
-                             MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE MBEDTLS_ECP_LIGHT
+                             MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED \
+                             MBEDTLS_SSL_TLS1_3_COMPATIBILITY_MODE
 requires_any_configs_enabled MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_ENABLED \
                              MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_PSK_EPHEMERAL_ENABLED
-run_test "TLS 1.3 G->m: EarlyData: psk*: feature is enabled, fail." \
-         "$P_SRV force_version=tls13 debug_level=4 max_early_data_size=$EARLY_DATA_INPUT_LEN $(get_srv_psk_list)" \
-         "$G_NEXT_CLI localhost --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+GROUP-ALL:-KX-ALL:+ECDHE-PSK:+DHE-PSK:+PSK \
-                      -d 10 -r --earlydata $EARLY_DATA_INPUT \
-                      --pskusername Client_identity --pskkey=6162636465666768696a6b6c6d6e6f70" \
+run_test "TLS 1.3 G->m: EarlyData: feature is enabled, fail." \
+         "$P_SRV force_version=tls13 debug_level=4 max_early_data_size=$EARLY_DATA_INPUT_LEN" \
+         "$G_NEXT_CLI localhost --priority=NORMAL:-VERS-ALL:+VERS-TLS1.3:+GROUP-ALL:+KX-ALL \
+                      -d 10 -r --earlydata $EARLY_DATA_INPUT " \
          1 \
          -s "ClientHello: early_data(42) extension exists."                 \
          -s "EncryptedExtensions: early_data(42) extension exists."         \
-         -s "NewSessionTicket: early_data(42) extension does not exist."
+         -s "NewSessionTicket: early_data(42) extension does not exist."    \
+         -s "Last error was: -29056 - SSL - Verification of the message MAC failed"