diff --git a/tests/suites/test_suite_ssl.data b/tests/suites/test_suite_ssl.data
index 7c2f03e..2c9d197 100644
--- a/tests/suites/test_suite_ssl.data
+++ b/tests/suites/test_suite_ssl.data
@@ -3490,3 +3490,24 @@
 Inject ClientHello - TLS 1.3 fragmented 4 + invalid type + 72 rejected
 depends_on:MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_SSL_TLS1_3_KEY_EXCHANGE_MODE_EPHEMERAL_ENABLED:MBEDTLS_SSL_HAVE_AES:MBEDTLS_MD_CAN_SHA256:MBEDTLS_SSL_HAVE_GCM:MBEDTLS_ECP_HAVE_SECP256R1:MBEDTLS_ECP_HAVE_SECP384R1:MBEDTLS_PK_CAN_ECDSA_SIGN:MBEDTLS_PK_CAN_ECDSA_VERIFY
 inject_client_content_on_the_wire:MBEDTLS_PK_ECDSA:MBEDTLS_SSL_CLIENT_HELLO:"1603030004010000481003030002015a160303004803030123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef00000213010100001d000a000400020017002b0003020304000d000400020403003300020000":"unknown record type":MBEDTLS_ERR_SSL_INVALID_RECORD
+
+Send large fragmented ClientHello: 4 bytes too large
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN:0:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: 1 byte too large
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 3:0:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: would fit without overhead #1
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 4:0:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: would fit without overhead #2
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 4:1:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: would fit without overhead #3
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 4:2:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: would fit without overhead #4
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 4:3:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
+
+Send large fragmented ClientHello: would fit without overhead #5
+send_large_fragmented_hello:MBEDTLS_SSL_IN_CONTENT_LEN - 4:4:"requesting more data than fits":MBEDTLS_ERR_SSL_BAD_INPUT_DATA
diff --git a/tests/suites/test_suite_ssl.function b/tests/suites/test_suite_ssl.function
index 9630fe0..c4d57f7 100644
--- a/tests/suites/test_suite_ssl.function
+++ b/tests/suites/test_suite_ssl.function
@@ -5088,3 +5088,115 @@
     PSA_DONE();
 }
 /* END_CASE */
+
+/* BEGIN_CASE depends_on:MBEDTLS_SSL_PROTO_TLS1_3:MBEDTLS_DEBUG_C:MBEDTLS_SSL_HANDSHAKE_WITH_CERT_ENABLED */
+void send_large_fragmented_hello(int hs_len_int, int first_frag_content_len_int,
+                                 char *log_pattern, int expected_ret)
+{
+    /* This function sends a long message (claiming to be a ClientHello)
+     * fragmented in 1-byte fragments (except the initial fragment).
+     * The purpose is to test how the stack reacts when receiving:
+     * - a message larger than our buffer;
+     * - a message smaller than our buffer, but where the intermediate size of
+     *   holding all the fragments (including overhead) is larger than our
+     *   buffer.
+     */
+    enum { BUFFSIZE = 16384 };
+    mbedtls_test_ssl_endpoint server, client;
+    mbedtls_platform_zeroize(&server, sizeof(server));
+    mbedtls_platform_zeroize(&client, sizeof(client));
+
+    mbedtls_test_handshake_test_options options;
+    mbedtls_test_init_handshake_options(&options);
+
+    mbedtls_test_ssl_log_pattern srv_pattern;
+    memset(&srv_pattern, 0, sizeof(srv_pattern));
+
+    unsigned char *first_frag = NULL;
+    int ret = -1;
+
+    size_t hs_len = (size_t) hs_len_int;
+    size_t first_frag_content_len = (size_t) first_frag_content_len_int;
+
+    PSA_INIT();
+
+    srv_pattern.pattern = log_pattern;
+    options.srv_log_obj = &srv_pattern;
+    options.srv_log_fun = mbedtls_test_ssl_log_analyzer;
+    mbedtls_debug_set_threshold(5);
+
+    ret = mbedtls_test_ssl_endpoint_init(&server, MBEDTLS_SSL_IS_SERVER,
+                                         &options, NULL, NULL, NULL);
+    TEST_EQUAL(ret,  0);
+
+    ret = mbedtls_test_ssl_endpoint_init(&client, MBEDTLS_SSL_IS_CLIENT,
+                                         &options, NULL, NULL, NULL);
+    TEST_EQUAL(ret,  0);
+
+    ret = mbedtls_test_mock_socket_connect(&server.socket, &client.socket,
+                                           BUFFSIZE);
+    TEST_EQUAL(ret,  0);
+
+    /* Make the server move past the initial dummy state */
+    ret = mbedtls_test_move_handshake_to_state(&client.ssl, &server.ssl,
+                                               MBEDTLS_SSL_CLIENT_HELLO);
+    TEST_EQUAL(ret, 0);
+
+    /* Prepare initial fragment */
+    const size_t first_len = 5 // record header, see below
+                             + 4 // handshake header, see balow
+                             + first_frag_content_len;
+    TEST_CALLOC(first_frag, first_len);
+    unsigned char *p = first_frag;
+    // record header
+    // record type: handshake
+    *p++ = 0x16,
+    // record version (actually common to TLS 1.2 and TLS 1.3)
+    *p++ = 0x03,
+    *p++ = 0x03,
+    // record length: two bytes
+    *p++ = (unsigned char) (((4 + first_frag_content_len) >> 8) & 0xff);
+    *p++ = (unsigned char) (((4 + first_frag_content_len) >> 0) & 0xff);
+    // handshake header
+    // handshake type: ClientHello
+    *p++ = 0x01,
+    // handshake length: three bytes
+    *p++ = (unsigned char) ((hs_len >> 16) & 0xff);
+    *p++ = (unsigned char) ((hs_len >>  8) & 0xff);
+    *p++ = (unsigned char) ((hs_len >>  0) & 0xff);
+    // handshake content: dummy value
+    memset(p, 0x2a, first_frag_content_len);
+
+    /* Send initial fragment and have the server process it. */
+    ret = mbedtls_test_mock_tcp_send_b(&client.socket, first_frag, first_len);
+    TEST_ASSERT(ret >= 0 && (size_t) ret == first_len);
+
+    ret = mbedtls_ssl_handshake_step(&server.ssl);
+    TEST_EQUAL(ret, MBEDTLS_ERR_SSL_WANT_READ);
+
+    /* Dummy 1-byte fragment to repeatedly send next */
+    const unsigned char next[] = {
+        0x16, 0x03, 0x03, 0x00, 0x01, // record header (see above)
+        0x2a, // Dummy handshake message content
+    };
+    for (size_t left = hs_len - first_frag_content_len; left != 0; left--) {
+        ret = mbedtls_test_mock_tcp_send_b(&client.socket, next, sizeof(next));
+        TEST_ASSERT(ret >= 0 && (size_t) ret == sizeof(next));
+
+        ret = mbedtls_ssl_handshake_step(&server.ssl);
+        if (ret != MBEDTLS_ERR_SSL_WANT_READ) {
+            break;
+        }
+    }
+    TEST_EQUAL(ret, expected_ret);
+    TEST_EQUAL(srv_pattern.counter, 1);
+
+exit:
+    mbedtls_test_free_handshake_options(&options);
+    mbedtls_test_ssl_endpoint_free(&server, NULL);
+    mbedtls_test_ssl_endpoint_free(&client, NULL);
+    mbedtls_debug_set_threshold(0);
+    mbedtls_free(first_frag);
+    PSA_DONE();
+}
+/* END_CASE */