diff --git a/testssl.sh b/testssl.sh
index 941c889..f8d1852 100755
--- a/testssl.sh
+++ b/testssl.sh
@@ -1570,51 +1570,102 @@ test_just_one(){
 # test for all ciphers locally configured (w/o distinguishing whether they are good or bad
 run_allciphers(){
      local tmpfile
-     local nr_ciphers
-     local -i sclient_success=0
-     local hexcode n ciph sslvers kx auth enc mac export
+     local -i nr_ciphers
+     local n sslvers auth mac export
+     local -a hexcode ciph kx enc export2
+     local -i i j parent child end_of_bundle round_num bundle_size num_bundles mod_check
+     local -a ciphers_found
      local dhlen
      local available
+     local ciphers_to_test
+
+     # get a list of all the cipher suites to test (only need the hexcode, ciph, kx, enc, and export values
+     nr_ciphers=0
+     $OPENSSL ciphers -V 'ALL:COMPLEMENTOFALL:@STRENGTH' 2>>$ERRFILE | (while read hexcode[nr_ciphers] n ciph[nr_ciphers] sslvers kx[nr_ciphers] auth enc[nr_ciphers] mac export2[nr_ciphers]; do
+         nr_ciphers=$nr_ciphers+1
+     done
 
-     nr_ciphers=$(count_ciphers "$($OPENSSL ciphers 'ALL:COMPLEMENTOFALL:@STRENGTH' 2>$ERRFILE)")
      outln
      pr_headlineln " Testing all $nr_ciphers locally available ciphers against the server, ordered by encryption strength "
      "$HAS_DH_BITS" || pr_warningln "    (Your $OPENSSL cannot show DH/ECDH bits)"
      outln
      neat_header
 
-     $OPENSSL ciphers -V 'ALL:COMPLEMENTOFALL:@STRENGTH' 2>>$ERRFILE | while read hexcode n ciph sslvers kx auth enc mac export; do
-     # FIXME: e.g. OpenSSL < 1.0 doesn't understand "-V" --> we can't do anything about it!
-          $OPENSSL s_client -cipher $ciph $STARTTLS $BUGS -connect $NODEIP:$PORT $PROXY $SNI >$TMPFILE 2>$ERRFILE </dev/null
-          sclient_connect_successful "$?" "$TMPFILE"
-          sclient_success=$?
-          if [[ "$sclient_success" -ne 0 ]] && ! "$SHOW_EACH_C"; then
-               continue       # no successful connect AND not verbose displaying each cipher
-          fi
-          normalize_ciphercode "$hexcode"
-          if [[ $kx == "Kx=ECDH" ]] || [[ $kx == "Kx=DH" ]] || [[ $kx == "Kx=EDH" ]]; then
-               dhlen=$(read_dhbits_from_file "$TMPFILE" quiet)
-               kx="$kx $dhlen"
-          fi
-          neat_list "$HEXC" "$ciph" "$kx" "$enc"
-          available=""
-          if "$SHOW_EACH_C"; then
-               if [[ "$sclient_success" -eq 0 ]]; then
-                    available="available"
-                    pr_cyan "  available"
-               else
-                    out "  not a/v"
-                    available="not a/v"
-               fi
-          fi
-          if "$SHOW_SIGALGO"; then
-               $OPENSSL x509 -noout -text -in $TMPFILE | awk -F':' '/Signature Algorithm/ { print $2 }' | head -1
-          else
-               outln
-          fi
-          fileout "cipher_$HEXC" "INFO" "$(neat_list "$HEXC" "$ciph" "$kx" "$enc") $available"
-          tmpfile_handle $FUNCNAME.txt
+     # Split ciphers into bundles of size 4**n, starting with an "n" that
+     # splits the ciphers into 4 bundles, and then reduing "n" by one in each
+     # round. Only test a bundle of 4**n ciphers against the server if it was
+     # part of a bundle of 4**(n+1) ciphers that included a cipher supported by
+     # the server. Continue until n=0.
+
+     # Determine bundle size that will result in their being exactly four bundles.
+     for((bundle_size=1;bundle_size<nr_ciphers;bundle_size*=4)); do
+         :
      done
+
+     # set ciphers_found[1] so that all bundles will be tested in round 0.
+     ciphers_found[1]=true
+     round_num=0
+
+     for ((bundle_size/=4;bundle_size>=1;bundle_size/=4)); do
+         # Note that since the number of ciphers isn't a power of 4, the number
+         # of bundles may be may be less than 4**(round_num+1), and the final
+         # bundle may have fewer than bundle_size ciphers.
+         num_bundles=$nr_ciphers/$bundle_size
+         mod_check=$nr_ciphers%$bundle_size
+         [[ $mod_check -ne 0 ]] && num_bundles=$num_bundles+1
+         for ((i=0;i<num_bundles;i++)); do
+             # parent=index of bundle from previous round that includes this bundle of ciphers
+             parent=4**$round_num+$i/4
+             # child=index for this bundle of ciphers
+             child=4*4**$round_num+$i
+             if ${ciphers_found[parent]}; then
+                 ciphers_to_test=""
+                 end_of_bundle=$i*$bundle_size+$bundle_size
+                 [[ $end_of_bundle -gt $nr_ciphers ]] && end_of_bundle=$nr_ciphers
+                 for ((j=i*bundle_size;j<end_of_bundle;j++)); do
+                     ciphers_to_test="${ciphers_to_test}:${ciph[j]}"
+                 done
+                 ciphers_found[child]=false
+                 $OPENSSL s_client -cipher "${ciphers_to_test:1}" $STARTTLS $BUGS -connect $NODEIP:$PORT $PROXY $SNI >$TMPFILE 2>$ERRFILE </dev/null
+                 sclient_connect_successful "$?" "$TMPFILE"
+                 [[ "$?" -eq 0 ]] && ciphers_found[child]=true
+             else
+                 # No need to test, since test of parent demonstrated none of these ciphers work.
+                 ciphers_found[child]=false
+             fi
+
+             # If this is a "leaf" of the test tree, then print out the results.
+             if [[ $bundle_size -eq 1 ]] && ( ${ciphers_found[child]} || "$SHOW_EACH_C"); then
+                 export=${export2[i]}
+                 normalize_ciphercode "${hexcode[i]}"
+                 if [[ ${kx[i]} == "Kx=ECDH" ]] || [[ ${kx[i]} == "Kx=DH" ]] || [[ ${kx[i]} == "Kx=EDH" ]]; then
+                     if ${ciphers_found[child]}; then
+                         dhlen=$(read_dhbits_from_file "$TMPFILE" quiet)
+                         kx[i]="${kx[i]} $dhlen"
+                     fi
+                 fi
+                 neat_list "$HEXC" "${ciph[i]}" "${kx[i]}" "${enc[i]}"
+                 available=""
+                 if "$SHOW_EACH_C"; then
+                     if ${ciphers_found[child]}; then
+                         available="available"
+                         pr_cyan "  available"
+                     else
+                         out "  not a/v"
+                         available="not a/v"
+                     fi
+                 fi
+                 if "$SHOW_SIGALGO" && ${ciphers_found[child]}; then
+                     $OPENSSL x509 -noout -text -in $TMPFILE | awk -F':' '/Signature Algorithm/ { print $2 }' | head -1
+                 else
+                     outln
+                 fi
+                 fileout "cipher_$HEXC" "INFO" "$(neat_list "$HEXC" "${ciph[i]}" "${kx[i]}" "${enc[i]}") $available"
+                 tmpfile_handle $FUNCNAME.txt
+             fi
+         done
+         round_num=round_num+1
+     done)
      outln
      return 0
 }