diff --git a/tests/scripts/analyze_outcomes.py b/tests/scripts/analyze_outcomes.py
index 29c41beba2..2bd4bd8162 100755
--- a/tests/scripts/analyze_outcomes.py
+++ b/tests/scripts/analyze_outcomes.py
@@ -43,7 +43,7 @@ class CoverageTask(outcome_analysis.CoverageTask):
             'DTLS cookie: enabled, IPv6',
             # Disabled due to OpenSSL bug.
             # https://github.com/openssl/openssl/issues/18887
-            'DTLS fragmenting: 3d, openssl client, DTLS 1.2',
+            'DTLS fragmenting: 3d, MTU=512, openssl client, DTLS 1.2',
             # We don't run ssl-opt.sh with Valgrind on the CI because
             # it's extremely slow. We don't intend to change this.
             'DTLS fragmenting: proxy MTU: auto-reduction (with valgrind)',
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 2c87e20278..7f36ab5c14 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -10360,6 +10360,37 @@ run_test    "DTLS fragmenting: both (MTU=512)" \
             -c "found fragmented DTLS handshake message" \
             -C "error"
 
+# Depending on the ciphersuite selected to encrypt the application data, the
+# maximum application data payload per record may be small with an MTU of 128.
+# For example, with TLS-ECDHE-ECDSA-WITH-AES-256-CBC-SHA384, this maximum is
+# 35 bytes. We therefore reduce the size of the client request and the server
+# response in this test.
+requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
+requires_max_content_len 2048
+run_test    "DTLS fragmenting: both (MTU=128)" \
+            -p "$P_PXY mtu=128" \
+            "$P_SRV dtls=1 debug_level=5 auth_mode=required \
+             crt_file=$DATA_FILES_PATH/server7_int-ca.crt \
+             key_file=$DATA_FILES_PATH/server7.key \
+             response_size=8 \
+             hs_timeout=2500-60000 \
+             mtu=128" \
+            "$P_CLI dtls=1 debug_level=2 \
+             crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
+             key_file=$DATA_FILES_PATH/server8.key \
+             request_size=8 \
+             hs_timeout=2500-60000 \
+             mtu=128" \
+            0 \
+            -s "found fragmented DTLS handshake message" \
+            -s "fragmenting Certificate handshake message" \
+            -s "fragmenting ServerKeyExchange handshake message" \
+            -c "found fragmented DTLS handshake message" \
+            -c "fragmenting ClientHello handshake message" \
+            -c "fragmenting Certificate handshake message" \
+            -c "fragmenting CertificateVerify handshake message" \
+            -C "error"
+
 # Test for automatic MTU reduction on repeated resend.
 # Forcing ciphersuite for this test to fit the MTU of 508 with full config.
 # The ratio of max/min timeout should ideally equal 4 to accept two
@@ -10736,7 +10767,7 @@ requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 requires_gnutls
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: gnutls server, DTLS 1.2" \
+run_test    "DTLS fragmenting: MTU=512, gnutls server, DTLS 1.2" \
             "$G_SRV -u" \
             "$P_CLI dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
@@ -10746,6 +10777,21 @@ run_test    "DTLS fragmenting: gnutls server, DTLS 1.2" \
             -c "fragmenting Certificate handshake message" \
             -C "error"
 
+requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
+requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
+requires_gnutls
+requires_max_content_len 2048
+run_test    "DTLS fragmenting: MTU=128, gnutls server, DTLS 1.2" \
+            "$G_NEXT_SRV -u" \
+            "$P_CLI dtls=1 debug_level=2 \
+             crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
+             key_file=$DATA_FILES_PATH/server8.key \
+             mtu=128 force_version=dtls12" \
+            0 \
+            -c "fragmenting ClientHello handshake message" \
+            -c "fragmenting Certificate handshake message" \
+            -C "error"
+
 # We use --insecure for the GnuTLS client because it expects
 # the hostname / IP it connects to to be the name used in the
 # certificate obtained from the server. Here, however, it
@@ -10758,7 +10804,7 @@ requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 requires_gnutls
 requires_not_i686
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: gnutls client, DTLS 1.2" \
+run_test    "DTLS fragmenting: MTU=512, gnutls client, DTLS 1.2" \
             "$P_SRV dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server7_int-ca.crt \
              key_file=$DATA_FILES_PATH/server7.key \
@@ -10770,7 +10816,7 @@ run_test    "DTLS fragmenting: gnutls client, DTLS 1.2" \
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: openssl server, DTLS 1.2" \
+run_test    "DTLS fragmenting: MTU=512, openssl server, DTLS 1.2" \
             "$O_SRV -dtls1_2 -verify 10" \
             "$P_CLI dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
@@ -10780,10 +10826,29 @@ run_test    "DTLS fragmenting: openssl server, DTLS 1.2" \
             -c "fragmenting Certificate handshake message" \
             -C "error"
 
+# Depending on the ciphersuite selected to encrypt the application data, the
+# maximum application data payload per record may be small with an MTU of 128.
+# For example, with TLS-ECDHE-ECDSA-WITH-AES-256-CBC-SHA384, this maximum is
+# 35 bytes. We therefore reduce the size of the client request in this test.
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: openssl client, DTLS 1.2" \
+run_test    "DTLS fragmenting: MTU=128, openssl server, DTLS 1.2" \
+            "$O_NEXT_SRV -dtls1_2 -verify 10" \
+            "$P_CLI dtls=1 debug_level=2 \
+             crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
+             key_file=$DATA_FILES_PATH/server8.key \
+             request_size=8 \
+             mtu=128 force_version=dtls12" \
+            0 \
+            -c "fragmenting ClientHello handshake message" \
+            -c "fragmenting Certificate handshake message" \
+            -C "error"
+
+requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
+requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
+requires_max_content_len 2048
+run_test    "DTLS fragmenting: MTU=512, openssl client, DTLS 1.2" \
             "$P_SRV dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server7_int-ca.crt \
              key_file=$DATA_FILES_PATH/server7.key \
@@ -10801,7 +10866,7 @@ requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 client_needs_more_time 4
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: 3d, gnutls server, DTLS 1.2" \
+run_test    "DTLS fragmenting: 3d, MTU=512, gnutls server, DTLS 1.2" \
             -p "$P_PXY drop=8 delay=8 duplicate=8" \
             "$G_NEXT_SRV -u" \
             "$P_CLI dgram_packing=0 dtls=1 debug_level=2 \
@@ -10812,12 +10877,29 @@ run_test    "DTLS fragmenting: 3d, gnutls server, DTLS 1.2" \
             -c "fragmenting Certificate handshake message" \
             -C "error"
 
+requires_gnutls_next
+requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
+requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
+client_needs_more_time 6
+requires_max_content_len 2048
+run_test    "DTLS fragmenting: 3d, MTU=128, gnutls server, DTLS 1.2" \
+            -p "$P_PXY drop=8 delay=8 duplicate=8" \
+            "$G_NEXT_SRV -u" \
+            "$P_CLI dgram_packing=0 dtls=1 debug_level=2 \
+             crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
+             key_file=$DATA_FILES_PATH/server8.key \
+             hs_timeout=250-60000 mtu=128 force_version=dtls12" \
+            0 \
+            -c "fragmenting ClientHello handshake message" \
+            -c "fragmenting Certificate handshake message" \
+            -C "error"
+
 requires_gnutls_next
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 client_needs_more_time 4
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: 3d, gnutls client, DTLS 1.2" \
+run_test    "DTLS fragmenting: 3d, MTU=512, gnutls client, DTLS 1.2" \
             -p "$P_PXY drop=8 delay=8 duplicate=8" \
             "$P_SRV dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server7_int-ca.crt \
@@ -10834,7 +10916,7 @@ requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 client_needs_more_time 4
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: 3d, openssl server, DTLS 1.2" \
+run_test    "DTLS fragmenting: 3d, MTU=512, openssl server, DTLS 1.2" \
             -p "$P_PXY drop=8 delay=8 duplicate=8" \
             "$O_NEXT_SRV -dtls1_2 -verify 10" \
             "$P_CLI dtls=1 debug_level=2 \
@@ -10845,6 +10927,28 @@ run_test    "DTLS fragmenting: 3d, openssl server, DTLS 1.2" \
             -c "fragmenting Certificate handshake message" \
             -C "error"
 
+# Depending on the ciphersuite selected to encrypt the application data, the
+# maximum application data payload per record may be small with an MTU of 128.
+# For example, with TLS-ECDHE-ECDSA-WITH-AES-256-CBC-SHA384, this maximum is
+# 35 bytes. We therefore reduce the size of the client request in this test.
+requires_openssl_next
+requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
+requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
+client_needs_more_time 4
+requires_max_content_len 2048
+run_test    "DTLS fragmenting: 3d, MTU=128, openssl server, DTLS 1.2" \
+            -p "$P_PXY drop=8 delay=8 duplicate=8" \
+            "$O_NEXT_SRV -dtls1_2 -verify 10" \
+            "$P_CLI dtls=1 debug_level=2 \
+             crt_file=$DATA_FILES_PATH/server8_int-ca2.crt \
+             key_file=$DATA_FILES_PATH/server8.key \
+             request_size=8 \
+             hs_timeout=250-60000 mtu=128 force_version=dtls12" \
+            0 \
+            -c "fragmenting ClientHello handshake message" \
+            -c "fragmenting Certificate handshake message" \
+            -C "error"
+
 ## the test below will time out with certain seed.
 ## The cause is an openssl bug (https://github.com/openssl/openssl/issues/18887)
 skip_next_test
@@ -10852,7 +10956,7 @@ requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled PSA_WANT_KEY_TYPE_RSA_KEY_PAIR_BASIC
 client_needs_more_time 4
 requires_max_content_len 2048
-run_test    "DTLS fragmenting: 3d, openssl client, DTLS 1.2" \
+run_test    "DTLS fragmenting: 3d, MTU=512, openssl client, DTLS 1.2" \
             -p "$P_PXY drop=8 delay=8 duplicate=8" \
             "$P_SRV dtls=1 debug_level=2 \
              crt_file=$DATA_FILES_PATH/server7_int-ca.crt \