diff --git a/doc/fate.texi b/doc/fate.texi
index 8450856015..2fa8c34c2d 100644
--- a/doc/fate.texi
+++ b/doc/fate.texi
@@ -223,6 +223,14 @@ meaning only while running the regression tests.
 Specify how many threads to use while running regression tests, it is
 quite useful to detect thread-related regressions.
 
+This variable may be set to the string "random", optionally followed by a
+number, like "random99", This will cause each test to use a random number of
+threads. If a number is specified, it is used as a maximum number of threads,
+otherwise 16 is the maximum.
+
+In case a test fails, the thread count used for it will be written into the
+errfile.
+
 @item THREAD_TYPE
 Specify which threading strategy test, either @samp{slice} or @samp{frame},
 by default @samp{slice+frame}
diff --git a/tests/fate-run.sh b/tests/fate-run.sh
index e12279e4cf..5a71ac001e 100755
--- a/tests/fate-run.sh
+++ b/tests/fate-run.sh
@@ -33,6 +33,15 @@ errfile="${outdir}/${test}.err"
 cmpfile="${outdir}/${test}.diff"
 repfile="${outdir}/${test}.rep"
 
+case $threads in
+    random*)
+        threads_max=${threads#random}
+        [ -z "$threads_max" ] && threads_max=16
+        threads=$(awk "BEGIN { print 1+int(rand() * $threads_max) }" < /dev/null)
+        ;;
+esac
+
+
 target_path(){
     test ${1} = ${1#/} && p=${target_path}/
     echo ${p}${1}
@@ -630,6 +639,7 @@ fi
 if [ $err -eq 0 ] && test $report_type = "standard" ; then
     unset cmpo erro
 else
+    echo "threads=$threads" >> "$errfile"
     cmpo="$($base64 <$cmpfile)"
     erro="$($base64 <$errfile)"
 fi