diff --git a/testssl.sh b/testssl.sh
index 65909eb..06f879e 100755
--- a/testssl.sh
+++ b/testssl.sh
@@ -1702,9 +1702,9 @@ check_revocation_crl() {
      [[ -n "$GOOD_CA_BUNDLE" ]] || return 0
      scheme="$(tolower "${crl%%://*}")"
      # The code for obtaining CRLs only supports LDAP, HTTP, and HTTPS URLs.
-     [[ "$scheme" == "http" ]] || [[ "$scheme" == "https" ]] || [[ "$scheme" == "ldap" ]] || return 0
+     [[ "$scheme" == http ]] || [[ "$scheme" == https ]] || [[ "$scheme" == ldap ]] || return 0
      tmpfile=$TEMPDIR/${NODE}-${NODEIP}.${crl##*\/} || exit $ERR_FCREATE
-     if [[ "$scheme" == "ldap" ]]; then
+     if [[ "$scheme" == ldap ]]; then
           ldap_get "$crl" "$tmpfile" "$jsonID"
           success=$?
      else
@@ -1737,7 +1737,7 @@ check_revocation_crl() {
           fileout "$jsonID" "OK" "not revoked"
      else
           retcode=$(awk '/error [1-9][0-9]? at [0-9]+ depth lookup:/ { if (!found) {print $2; found=1} }' "${tmpfile%%.crl}.err")
-          if [[ "$retcode" == "23" ]]; then # see verify_retcode_helper()
+          if [[ "$retcode" == 23 ]]; then # see verify_retcode_helper()
                out ", "
                pr_svrty_critical "revoked"
                fileout "$jsonID" "CRITICAL" "revoked"
@@ -4866,7 +4866,8 @@ run_protocols() {
      local lines nr_ciphers_detected
      local tls13_ciphers_to_test=""
      local i drafts_offered=""  drafts_offered_str="" supported_versions debug_recomm=""
-     local -i ret=0 subret=0
+     local -i ret=0 subret=0 ret_val_tls13=0
+     local offers_tls13=false
      local jsonID="SSLv2"
 
      outln; pr_headline " Testing protocols "
@@ -5027,8 +5028,8 @@ run_protocols() {
           run_prototest_openssl "-tls1"
      fi
      case $? in
-          0)   outln "offered"
-               fileout "$jsonID" "INFO" "offered"
+          0)   pr_svrty_low "offered" ; outln " (deprecated)"
+               fileout "$jsonID" "LOW" "offered (deprecated)"
                latest_supported="0301"
                latest_supported_string="TLSv1.0"
                add_tls_offered tls1 yes
@@ -5101,8 +5102,8 @@ run_protocols() {
           run_prototest_openssl "-tls1_1"
      fi
      case $? in
-          0)   outln "offered"
-               fileout "$jsonID" "INFO" "offered"
+          0)   pr_svrty_low "offered" ; outln " (deprecated)"
+               fileout "$jsonID" "LOW" "offered (deprecated)"
                latest_supported="0302"
                latest_supported_string="TLSv1.1"
                add_tls_offered tls1_1 yes
@@ -5170,6 +5171,39 @@ run_protocols() {
                ;;
      esac
 
+     # Now, we are doing a basic/pre test for TLS 1.3 in order not to penalize servers (medium)
+     # running TLS 1.3 only when TLS 1.2 is not offered.  0 and 5 are the return codes for
+     # TLS 1.3 support (kind of, including deprecated pre-versions of TLS 1.3)
+     if "$using_sockets"; then
+          # Need to ensure that at most 128 ciphers are included in ClientHello.
+          # If the TLSv1.2 test was successful, then use the 5 TLSv1.3 ciphers
+          # plus the cipher selected in the TLSv1.2 test. If the TLSv1.2 test was
+          # not successful, then just use the 5 TLSv1.3 ciphers plus the list of
+          # ciphers used in all of the previous tests ($TLS_CIPHER).
+          if [[ $subret -eq 0 ]] || [[ $subret -eq 2 ]]; then
+               tls13_ciphers_to_test="$(get_cipher "$TEMPDIR/$NODEIP.parse_tls_serverhello.txt")"
+               if [[ "$tls13_ciphers_to_test" == TLS_* ]] || [[ "$tls13_ciphers_to_test" == SSL_* ]]; then
+                    tls13_ciphers_to_test="$(rfc2hexcode "$tls13_ciphers_to_test")"
+               else
+                    tls13_ciphers_to_test="$(openssl2hexcode "$tls13_ciphers_to_test")"
+               fi
+          fi
+          if [[ ${#tls13_ciphers_to_test} -eq 9 ]]; then
+               tls13_ciphers_to_test="$TLS13_CIPHER, ${tls13_ciphers_to_test:2:2},${tls13_ciphers_to_test:7:2}, 00,ff"
+          else
+               tls13_ciphers_to_test="$TLS13_CIPHER,$TLS_CIPHER"
+          fi
+          tls_sockets "04" "$tls13_ciphers_to_test"
+     else
+          run_prototest_openssl "-tls1_3"
+     fi
+     ret_val_tls13=$?
+     if [[ $ret_val_tls13 -eq 0 ]] || [[ $ret_val_tls13 -eq 5 ]]; then
+          offers_tls13=true             # This variable comes in handy for further if statements below
+     fi
+     # Done with pretesting TLS 1.3. Normally we should/could reverse the order for the protocols -- or
+     # keep the order and mute the output, until we can make a final verdict
+
      pr_bold " TLS 1.2    ";
      jsonID="TLS1_2"
      if "$using_sockets"; then
@@ -5190,19 +5224,31 @@ run_protocols() {
                latest_supported="0303"
                latest_supported_string="TLSv1.2"
                add_tls_offered tls1_2 yes
-               ;;                                  # GCM cipher in TLS 1.2: very good!
-          1)   pr_svrty_medium "not offered"
-               add_tls_offered tls1_2 no
+               ;;                                                     # GCM cipher in TLS 1.2: very good!
+          1)   add_tls_offered tls1_2 no
+               if "$offers_tls13"; then
+                    out "not offered"
+               else
+                    pr_svrty_medium "not offered"
+               fi
                if ! "$using_sockets" || [[ -z $latest_supported ]]; then
                     outln
-                    fileout "$jsonID" "MEDIUM" "not offered" # no GCM, penalty
+                    if "$offers_tls13"; then
+                         fileout "$jsonID" "INFO" "not offered"
+                    else
+                         fileout "$jsonID" "MEDIUM" "not offered"     # TLS 1.3, no TLS 1.2 --> no GCM, penalty
+                    fi
                else
                     prln_svrty_critical " -- connection failed rather than downgrading to $latest_supported_string"
                     fileout "$jsonID" "CRITICAL" "connection failed rather than downgrading to $latest_supported_string"
                fi
                ;;
-          2)   pr_svrty_medium "not offered"
-               add_tls_offered tls1_2 no
+          2)   add_tls_offered tls1_2 no
+               if "$offers_tls13"; then
+                    out "not offered"
+               else
+                    pr_svrty_medium "not offered"
+               fi
                if [[ "$DETECTED_TLS_VERSION" == 0300 ]]; then
                     detected_version_string="SSLv3"
                elif [[ "$DETECTED_TLS_VERSION" == 03* ]]; then
@@ -5229,7 +5275,7 @@ run_protocols() {
                fi
                ;;
            3)  out "not offered, "
-               fileout "$jsonID" "OK" "not offered"
+               fileout "$jsonID" "INFO" "not offered"
                add_tls_offered tls1_2 no
                pr_warning "TLS downgraded to STARTTLS plaintext"; outln
                fileout "$jsonID" "WARN" "TLS downgraded to STARTTLS plaintext"
@@ -5260,30 +5306,7 @@ run_protocols() {
 
      pr_bold " TLS 1.3    ";
      jsonID="TLS1_3"
-     if "$using_sockets"; then
-          # Need to ensure that at most 128 ciphers are included in ClientHello.
-          # If the TLSv1.2 test was successful, then use the 5 TLSv1.3 ciphers
-          # plus the cipher selected in the TLSv1.2 test. If the TLSv1.2 test was
-          # not successful, then just use the 5 TLSv1.3 ciphers plus the list of
-          # ciphers used in all of the previous tests ($TLS_CIPHER).
-          if [[ $subret -eq 0 ]] || [[ $subret -eq 2 ]]; then
-               tls13_ciphers_to_test="$(get_cipher "$TEMPDIR/$NODEIP.parse_tls_serverhello.txt")"
-               if [[ "$tls13_ciphers_to_test" == TLS_* ]] || [[ "$tls13_ciphers_to_test" == SSL_* ]]; then
-                    tls13_ciphers_to_test="$(rfc2hexcode "$tls13_ciphers_to_test")"
-               else
-                    tls13_ciphers_to_test="$(openssl2hexcode "$tls13_ciphers_to_test")"
-               fi
-          fi
-          if [[ ${#tls13_ciphers_to_test} -eq 9 ]]; then
-               tls13_ciphers_to_test="$TLS13_CIPHER, ${tls13_ciphers_to_test:2:2},${tls13_ciphers_to_test:7:2}, 00,ff"
-          else
-               tls13_ciphers_to_test="$TLS13_CIPHER,$TLS_CIPHER"
-          fi
-          tls_sockets "04" "$tls13_ciphers_to_test"
-     else
-          run_prototest_openssl "-tls1_3"
-     fi
-     case $? in
+     case $ret_val_tls13 in
           0)   if ! "$using_sockets"; then
                     prln_svrty_best "offered (OK)"
                     fileout "$jsonID" "OK" "offered"
@@ -5375,33 +5398,35 @@ run_protocols() {
                latest_supported_string="TLSv1.3"
                add_tls_offered tls1_3 yes
                ;;
-          1)   out "not offered"
+          1)   pr_svrty_low "not offered"
                if ! "$using_sockets" || [[ -z $latest_supported ]]; then
                     outln
-                    fileout "$jsonID" "INFO" "not offered"
+                    fileout "$jsonID" "LOW" "not offered"
                else
                     prln_svrty_critical " -- connection failed rather than downgrading to $latest_supported_string"
                     fileout "$jsonID" "CRITICAL" "connection failed rather than downgrading to $latest_supported_string"
                fi
                add_tls_offered tls1_3 no
                ;;
-          2)   out "not offered"
-               if [[ "$DETECTED_TLS_VERSION" == 0300 ]]; then
+          2)   if [[ "$DETECTED_TLS_VERSION" == 0300 ]]; then
                     detected_version_string="SSLv3"
                elif [[ "$DETECTED_TLS_VERSION" == 03* ]]; then
                     detected_version_string="TLSv1.$((0x$DETECTED_TLS_VERSION-0x0301))"
                fi
                if [[ "$DETECTED_TLS_VERSION" == "$latest_supported" ]]; then
                     [[ $DEBUG -ge 1 ]] && tm_out " -- downgraded"
-                    outln
-                    fileout "$jsonID" "INFO" "not offered and downgraded to a weaker protocol"
+                    outln "not offered and downgraded to a weaker protocol"
+                    fileout "$jsonID" "INFO" "not offered + downgraded to weaker protocol"
                elif [[ "$DETECTED_TLS_VERSION" == 03* ]] && [[ 0x$DETECTED_TLS_VERSION -lt 0x$latest_supported ]]; then
+                    out "not offered"
                     prln_svrty_critical " -- server supports $latest_supported_string, but downgraded to $detected_version_string"
                     fileout "$jsonID" "CRITICAL" "not offered, and downgraded to $detected_version_string rather than $latest_supported_string"
                elif [[ "$DETECTED_TLS_VERSION" == 03* ]] && [[ 0x$DETECTED_TLS_VERSION -gt 0x0304 ]]; then
+                    out "not offered"
                     prln_svrty_critical " -- server responded with higher version number ($detected_version_string) than requested by client"
                     fileout "$jsonID" "CRITICAL" "not offered, server responded with higher version number ($detected_version_string) than requested by client"
                else
+                    out "not offered"
                     prln_svrty_critical " -- server responded with version number ${DETECTED_TLS_VERSION:0:2}.${DETECTED_TLS_VERSION:2:2}"
                     fileout "$jsonID" "CRITICAL" "server responded with version number ${DETECTED_TLS_VERSION:0:2}.${DETECTED_TLS_VERSION:2:2}"
                fi