diff --git a/scripts/output_env.sh b/scripts/output_env.sh
index 5356132..63628e7 100755
--- a/scripts/output_env.sh
+++ b/scripts/output_env.sh
@@ -192,20 +192,6 @@
 print_version "$GNUTLS_SERV" "--version" "default" "head -n 1"
 echo
 
-if [ -n "${GNUTLS_LEGACY_CLI+set}" ]; then
-    print_version "$GNUTLS_LEGACY_CLI" "--version" "legacy" "head -n 1"
-else
-     echo " * gnutls-cli (legacy): Not configured."
-fi
-echo
-
-if [ -n "${GNUTLS_LEGACY_SERV+set}" ]; then
-    print_version "$GNUTLS_LEGACY_SERV" "--version" "legacy" "head -n 1"
-else
-    echo " * gnutls-serv (legacy): Not configured."
-fi
-echo
-
 echo " * Installed asan versions:"
 if type dpkg-query >/dev/null 2>/dev/null; then
     if ! dpkg-query -f '${Status} ${Package}: ${Version}\n' -W 'libasan*' |
diff --git a/tests/compat.sh b/tests/compat.sh
index ba8465b..de9dc40 100755
--- a/tests/compat.sh
+++ b/tests/compat.sh
@@ -110,6 +110,7 @@
 EXCLUDE='NULL\|DES\|RC4\|ARCFOUR\|ARIA\|CHACHA20-POLY1305'
 VERBOSE=""
 MEMCHECK=0
+PRESERVE_LOGS=0
 PEERS="OpenSSL$PEER_GNUTLS mbedTLS"
 
 # hidden option: skip DTLS with OpenSSL
@@ -131,6 +132,7 @@
     printf "     --list-test-case\tList all potential test cases (No Execution)\n"
     printf "     --outcome-file\tFile where test outcomes are written\n"
     printf "                   \t(default: \$MBEDTLS_TEST_OUTCOME_FILE, none if empty)\n"
+    printf "     --preserve-logs\tPreserve logs of successful tests as well\n"
 }
 
 # print_test_case <CLIENT> <SERVER> <STANDARD_CIPHER_SUITE>
@@ -198,6 +200,9 @@
             --outcome-file)
                 shift; MBEDTLS_TEST_OUTCOME_FILE=$1
                 ;;
+            --preserve-logs)
+                PRESERVE_LOGS=1
+                ;;
             -h|--help)
                 print_usage
                 exit 0
@@ -648,7 +653,16 @@
             ;;
 
         "RSA")
-            if [ `minor_ver "$MODE"` -gt 0 ]
+            # TLS-RSA-WITH-NULL-SHA256 is a (D)TLS 1.2-only cipher suite,
+            # like all SHA256 cipher suites. But Mbed TLS supports it with
+            # (D)TLS 1.0 and 1.1 as well. So do ancient versions of GnuTLS,
+            # but this was considered a bug which was fixed in GnuTLS 3.4.7.
+            # Check the GnuTLS support list to see what the protocol version
+            # requirement is for that cipher suite.
+            if [ `minor_ver "$MODE"` -ge 3 ] || {
+                   [ `minor_ver "$MODE"` -gt 0 ] &&
+                   $GNUTLS_CLI --list | grep -q '^TLS_RSA_NULL_SHA256.*0$'
+               }
             then
                 M_CIPHERS="$M_CIPHERS                           \
                     TLS-RSA-WITH-NULL-SHA256                    \
@@ -972,7 +986,7 @@
     fi
 
     M_SERVER_ARGS="server_port=$PORT server_addr=0.0.0.0 force_version=$MODE arc4=1"
-    O_SERVER_ARGS="-accept $PORT -cipher NULL,ALL -$O_MODE"
+    O_SERVER_ARGS="-accept $PORT -cipher ALL,COMPLEMENTOFALL -$O_MODE"
     G_SERVER_ARGS="-p $PORT --http $G_MODE"
     G_SERVER_PRIO="NORMAL:${G_PRIO_CCM}+ARCFOUR-128:+NULL:+MD5:+PSK:+DHE-PSK:+ECDHE-PSK:+SHA256:+SHA384:+RSA-PSK:-VERS-TLS-ALL:$G_PRIO_MODE"
 
@@ -1218,12 +1232,16 @@
     fi
 }
 
+save_logs() {
+    cp $SRV_OUT c-srv-${TESTS}.log
+    cp $CLI_OUT c-cli-${TESTS}.log
+}
+
 # display additional information if test case fails
 report_fail() {
     FAIL_PROMPT="outputs saved to c-srv-${TESTS}.log, c-cli-${TESTS}.log"
     record_outcome "FAIL" "$FAIL_PROMPT"
-    cp $SRV_OUT c-srv-${TESTS}.log
-    cp $CLI_OUT c-cli-${TESTS}.log
+    save_logs
     echo "  ! $FAIL_PROMPT"
 
     if [ "${LOG_FAILURE_ON_STDOUT:-0}" != 0 ]; then
@@ -1349,6 +1367,9 @@
     case $RESULT in
         "0")
             record_outcome "PASS"
+            if [ "$PRESERVE_LOGS" -gt 0 ]; then
+                save_logs
+            fi
             ;;
         "1")
             record_outcome "SKIP"
diff --git a/tests/scripts/all.sh b/tests/scripts/all.sh
index afb4a9d..aeaaec9 100755
--- a/tests/scripts/all.sh
+++ b/tests/scripts/all.sh
@@ -50,10 +50,14 @@
 #   * G++
 #   * arm-gcc and mingw-gcc
 #   * ArmCC 5 and ArmCC 6, unless invoked with --no-armcc
-#   * OpenSSL and GnuTLS command line tools, recent enough for the
-#     interoperability tests. If they don't support SSLv3 then a legacy
-#     version of these tools must be present as well (search for LEGACY
-#     below).
+#   * OpenSSL and GnuTLS command line tools, in suitable versions for the
+#     interoperability tests. The following are the official versions at the
+#     time of writing:
+#     * GNUTLS_{CLI,SERV} = 3.4.10
+#     * GNUTLS_NEXT_{CLI,SERV} = 3.7.2
+#     * OPENSSL_LEGACY = 1.0.1j
+#     * OPENSSL = 1.0.2g (without Debian/Ubuntu patches)
+#     * OPENSSL_NEXT = 1.1.1a
 # See the invocation of check_tools below for details.
 #
 # This script must be invoked from the toplevel directory of a git
@@ -168,8 +172,6 @@
     : ${OPENSSL_NEXT:="$OPENSSL"}
     : ${GNUTLS_CLI:="gnutls-cli"}
     : ${GNUTLS_SERV:="gnutls-serv"}
-    : ${GNUTLS_LEGACY_CLI:="$GNUTLS_CLI"}
-    : ${GNUTLS_LEGACY_SERV:="$GNUTLS_SERV"}
     : ${OUT_OF_SOURCE_DIR:=./mbedtls_out_of_source_build}
     : ${ARMC5_BIN_DIR:=/usr/bin}
     : ${ARMC6_BIN_DIR:=/usr/bin}
@@ -286,8 +288,6 @@
      --gcc-latest=<GCC_latest_path>             Latest version of GCC available
      --gnutls-cli=<GnuTLS_cli_path>             GnuTLS client executable to use for most tests.
      --gnutls-serv=<GnuTLS_serv_path>           GnuTLS server executable to use for most tests.
-     --gnutls-legacy-cli=<GnuTLS_cli_path>      GnuTLS client executable to use for legacy tests.
-     --gnutls-legacy-serv=<GnuTLS_serv_path>    GnuTLS server executable to use for legacy tests.
      --openssl=<OpenSSL_path>                   OpenSSL executable to use for most tests.
      --openssl-legacy=<OpenSSL_path>            OpenSSL executable to use for legacy tests e.g. SSLv3.
      --openssl-next=<OpenSSL_path>              OpenSSL executable to use for recent things like ARIA
@@ -435,8 +435,8 @@
             --gcc-earliest) shift; GCC_EARLIEST="$1";;
             --gcc-latest) shift; GCC_LATEST="$1";;
             --gnutls-cli) shift; GNUTLS_CLI="$1";;
-            --gnutls-legacy-cli) shift; GNUTLS_LEGACY_CLI="$1";;
-            --gnutls-legacy-serv) shift; GNUTLS_LEGACY_SERV="$1";;
+            --gnutls-legacy-cli) shift;; # ignored for backward compatibility
+            --gnutls-legacy-serv) shift;; # ignored for backward compatibility
             --gnutls-serv) shift; GNUTLS_SERV="$1";;
             --help|-h) usage; exit;;
             --keep-going|-k) KEEP_GOING=1;;
@@ -709,8 +709,6 @@
     echo "OPENSSL_NEXT: $OPENSSL_NEXT"
     echo "GNUTLS_CLI: $GNUTLS_CLI"
     echo "GNUTLS_SERV: $GNUTLS_SERV"
-    echo "GNUTLS_LEGACY_CLI: $GNUTLS_LEGACY_CLI"
-    echo "GNUTLS_LEGACY_SERV: $GNUTLS_LEGACY_SERV"
     echo "ARMC5_BIN_DIR: $ARMC5_BIN_DIR"
     echo "ARMC6_BIN_DIR: $ARMC6_BIN_DIR"
 }
@@ -736,11 +734,8 @@
             fi
             set "$@" OPENSSL="$OPENSSL" OPENSSL_LEGACY="$OPENSSL_LEGACY"
             set "$@" GNUTLS_CLI="$GNUTLS_CLI" GNUTLS_SERV="$GNUTLS_SERV"
-            set "$@" GNUTLS_LEGACY_CLI="$GNUTLS_LEGACY_CLI"
-            set "$@" GNUTLS_LEGACY_SERV="$GNUTLS_LEGACY_SERV"
             check_tools "$OPENSSL" "$OPENSSL_LEGACY" "$OPENSSL_NEXT" \
-                        "$GNUTLS_CLI" "$GNUTLS_SERV" \
-                        "$GNUTLS_LEGACY_CLI" "$GNUTLS_LEGACY_SERV"
+                        "$GNUTLS_CLI" "$GNUTLS_SERV"
             ;;
     esac
 
@@ -1031,8 +1026,7 @@
     make test
 
     msg "build: SSLv3 - compat.sh (ASan build)" # ~ 6 min
-    tests/compat.sh -m 'tls1 tls1_1 tls12 dtls1 dtls12'
-    env OPENSSL="$OPENSSL_LEGACY" tests/compat.sh -m 'ssl3'
+    tests/compat.sh -m 'ssl3 tls1 tls1_1 tls12 dtls1 dtls12'
 
     msg "build: SSLv3 - ssl-opt.sh (ASan build)" # ~ 6 min
     tests/ssl-opt.sh
@@ -1590,8 +1584,11 @@
     msg "test: ssl-opt.sh default, ECJPAKE, SSL async (full config)" # ~ 1s
     tests/ssl-opt.sh -f 'Default\|ECJPAKE\|SSL async private'
 
-    msg "test: compat.sh RC4, DES, 3DES & NULL (full config)" # ~ 2 min
-    env OPENSSL="$OPENSSL_LEGACY" GNUTLS_CLI="$GNUTLS_LEGACY_CLI" GNUTLS_SERV="$GNUTLS_LEGACY_SERV" tests/compat.sh -e '^$' -f 'NULL\|DES\|RC4\|ARCFOUR'
+    msg "test: compat.sh RC4, 3DES & NULL (full config)" # ~ 2min
+    tests/compat.sh -e '^$' -f 'NULL\|3DES\|DES-CBC3\|RC4\|ARCFOUR'
+
+    msg "test: compat.sh single-DES (full config)" # ~ 30s
+    env OPENSSL="$OPENSSL_LEGACY" tests/compat.sh -e '3DES\|DES-CBC3' -f 'DES'
 
     msg "test: compat.sh ARIA + ChachaPoly"
     env OPENSSL="$OPENSSL_NEXT" tests/compat.sh -e '^$' -f 'ARIA\|CHACHA'
@@ -1881,8 +1878,11 @@
     msg "test: compat.sh default (full minus MBEDTLS_USE_PSA_CRYPTO)"
     tests/compat.sh
 
-    msg "test: compat.sh RC4, DES & NULL (full minus MBEDTLS_USE_PSA_CRYPTO)"
-    env OPENSSL="$OPENSSL_LEGACY" GNUTLS_CLI="$GNUTLS_LEGACY_CLI" GNUTLS_SERV="$GNUTLS_LEGACY_SERV" tests/compat.sh -e '3DES\|DES-CBC3' -f 'NULL\|DES\|RC4\|ARCFOUR'
+    msg "test: compat.sh RC4, 3DES & NULL (full minus MBEDTLS_USE_PSA_CRYPTO)"
+    tests/compat.sh -e '^$' -f 'NULL\|3DES\|DES-CBC3\|RC4\|ARCFOUR'
+
+    msg "test: compat.sh single-DES (full minus MBEDTLS_USE_PSA_CRYPTO)"
+    env OPENSSL="$OPENSSL_LEGACY" tests/compat.sh -e '3DES\|DES-CBC3' -f 'DES'
 
     msg "test: compat.sh ARIA + ChachaPoly (full minus MBEDTLS_USE_PSA_CRYPTO)"
     env OPENSSL="$OPENSSL_NEXT" tests/compat.sh -e '^$' -f 'ARIA\|CHACHA'
diff --git a/tests/scripts/basic-build-test.sh b/tests/scripts/basic-build-test.sh
index 196ce45..970abfa 100755
--- a/tests/scripts/basic-build-test.sh
+++ b/tests/scripts/basic-build-test.sh
@@ -51,8 +51,6 @@
 : ${OPENSSL_LEGACY:="$OPENSSL"}
 : ${GNUTLS_CLI:="gnutls-cli"}
 : ${GNUTLS_SERV:="gnutls-serv"}
-: ${GNUTLS_LEGACY_CLI:="$GNUTLS_CLI"}
-: ${GNUTLS_LEGACY_SERV:="$GNUTLS_SERV"}
 
 # Used to make ssl-opt.sh deterministic.
 #
@@ -81,8 +79,6 @@
     OPENSSL_LEGACY="$OPENSSL_LEGACY"         \
     GNUTLS_CLI="$GNUTLS_CLI"                 \
     GNUTLS_SERV="$GNUTLS_SERV"               \
-    GNUTLS_LEGACY_CLI="$GNUTLS_LEGACY_CLI"   \
-    GNUTLS_LEGACY_SERV="$GNUTLS_LEGACY_SERV" \
     scripts/output_env.sh
 echo
 
@@ -120,17 +116,12 @@
 # Step 2c - Compatibility tests (keep going even if some tests fail)
 echo '################ compat.sh ################'
 {
-    echo '#### compat.sh: Default versions'
-    sh compat.sh -m 'tls1 tls1_1 tls12 dtls1 dtls12'
-    echo
-
-    echo '#### compat.sh: legacy (SSLv3)'
-    OPENSSL="$OPENSSL_LEGACY" sh compat.sh -m 'ssl3'
+    echo '#### compat.sh: Default ciphers'
+    sh compat.sh -m 'ssl3 tls1 tls1_1 tls12 dtls1 dtls12'
     echo
 
     echo '#### compat.sh: legacy (null, DES, RC4)'
     OPENSSL="$OPENSSL_LEGACY" \
-    GNUTLS_CLI="$GNUTLS_LEGACY_CLI" GNUTLS_SERV="$GNUTLS_LEGACY_SERV" \
     sh compat.sh -e '^$' -f 'NULL\|DES\|RC4\|ARCFOUR'
     echo
 
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 3a27aac..4b6b695 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -81,14 +81,6 @@
 
 # alternative versions of OpenSSL and GnuTLS (no default path)
 
-if [ -n "${OPENSSL_LEGACY:-}" ]; then
-    O_LEGACY_SRV="$OPENSSL_LEGACY s_server -www -cert data_files/server5.crt -key data_files/server5.key"
-    O_LEGACY_CLI="echo 'GET / HTTP/1.0' | $OPENSSL_LEGACY s_client"
-else
-    O_LEGACY_SRV=false
-    O_LEGACY_CLI=false
-fi
-
 if [ -n "${OPENSSL_NEXT:-}" ]; then
     O_NEXT_SRV="$OPENSSL_NEXT s_server -www -cert data_files/server5.crt -key data_files/server5.key"
     O_NEXT_CLI="echo 'GET / HTTP/1.0' | $OPENSSL_NEXT s_client"
@@ -456,20 +448,6 @@
     fi
 }
 
-# skip next test if OpenSSL-legacy isn't available
-requires_openssl_legacy() {
-    if [ -z "${OPENSSL_LEGACY_AVAILABLE:-}" ]; then
-        if which "${OPENSSL_LEGACY:-}" >/dev/null 2>&1; then
-            OPENSSL_LEGACY_AVAILABLE="YES"
-        else
-            OPENSSL_LEGACY_AVAILABLE="NO"
-        fi
-    fi
-    if [ "$OPENSSL_LEGACY_AVAILABLE" = "NO" ]; then
-        SKIP_NEXT="YES"
-    fi
-}
-
 requires_openssl_next() {
     if [ -z "${OPENSSL_NEXT_AVAILABLE:-}" ]; then
         if which "${OPENSSL_NEXT:-}" >/dev/null 2>&1; then
@@ -1502,11 +1480,6 @@
 G_SRV="$G_SRV -p $SRV_PORT"
 G_CLI="$G_CLI -p +SRV_PORT"
 
-if [ -n "${OPENSSL_LEGACY:-}" ]; then
-    O_LEGACY_SRV="$O_LEGACY_SRV -accept $SRV_PORT -dhparam data_files/dhparams.pem"
-    O_LEGACY_CLI="$O_LEGACY_CLI -connect 127.0.0.1:+SRV_PORT"
-fi
-
 # Newer versions of OpenSSL have a syntax to enable all "ciphers", even
 # low-security ones. This covers not just cipher suites but also protocol
 # versions. It is necessary, for example, to use (D)TLS 1.0/1.1 on