diff --git a/test/units/testsuite-36.sh b/test/units/testsuite-36.sh
index 94fd927a5d..b684011785 100755
--- a/test/units/testsuite-36.sh
+++ b/test/units/testsuite-36.sh
@@ -34,8 +34,9 @@ journalCursorFile="jounalCursorFile"
 
 startStrace() {
     coproc strace -qq -p 1 -o "$straceLog" -e set_mempolicy -s 1024 ${1:+"$1"}
-    # Wait for strace to properly "initialize"
-    sleep $sleepAfterStart
+    # Wait for strace to properly "initialize", i.e. until PID 1 has the TracerPid
+    # field set to the current strace's PID
+    while ! awk -v spid="$COPROC_PID" '/^TracerPid:/ {exit !($2 == spid);}' /proc/1/status; do sleep 0.1; done
 }
 
 stopStrace() {