diff --git a/bin/tests/system/additional/tests.sh b/bin/tests/system/additional/tests.sh
index 27dca50e79..e434474ab1 100644
--- a/bin/tests/system/additional/tests.sh
+++ b/bin/tests/system/additional/tests.sh
@@ -373,6 +373,8 @@ fi
 n=$((n + 1))
 echo_i "testing NS handling in ANY responses (recursive) ($n)"
 ret=0
+# pre-cache the address record
+$DIG $DIGOPTS -t A ns1.rt.example @10.53.0.3 >/dev/null || ret=1
 $DIG $DIGOPTS -t ANY rt.example @10.53.0.3 >dig.out.$n || ret=1
 grep "AUTHORITY: 0" dig.out.$n >/dev/null || ret=1
 grep "NS[ 	]*ns" dig.out.$n >/dev/null || ret=1
diff --git a/bin/tests/system/cookie/tests.sh b/bin/tests/system/cookie/tests.sh
index 5c08beb05c..36ba494030 100755
--- a/bin/tests/system/cookie/tests.sh
+++ b/bin/tests/system/cookie/tests.sh
@@ -566,7 +566,7 @@ sys.exit(1)'; then
   ret=0
   pat='10\.53\.0\.10 .*\[cookie=................................\] \[ttl'
   # prime EDNS COOKIE state
-  $DIG $DIGOPTS @10.53.0.1 tsig. >dig.out.test$n.1 || ret=1
+  $DIG $DIGOPTS @10.53.0.1 NS tsig. >dig.out.test$n.1 || ret=1
   grep "status: NOERROR" dig.out.test$n.1 >/dev/null || ret=1
   rndc_dumpdb ns1
   # prime cache with NS response for QNAME minimisation
diff --git a/bin/tests/system/resolver/tests.sh b/bin/tests/system/resolver/tests.sh
index bd8f8972c2..e9affc1cb4 100755
--- a/bin/tests/system/resolver/tests.sh
+++ b/bin/tests/system/resolver/tests.sh
@@ -76,13 +76,21 @@ n=$((n + 1))
 echo_i "checking that the timeout didn't skew the resolver responses counters and did update the timeout counter ($n)"
 ret=0
 rndccmd 10.53.0.1 stats || ret=1
+# the timeout query triggers two extra queries, so we expect a small increase
 grep -F 'responses received' ns1/named.stats >ns1/named.stats.responses-after || true
+read before _ <ns1/named.stats.responses-before || true
+read after _ <ns1/named.stats.responses-after || true
+[ $((after - before)) -lt 3 ] || ret=1
 grep -F 'queries with RTT' ns1/named.stats >ns1/named.stats.rtt-after || true
+read before _ <ns1/named.stats.rtt-before || true
+read after _ <ns1/named.stats.rtt-after || true
+[ $((after - before)) -lt 3 ] || ret=1
+# ...but the timeout counter should increase by more
 grep -F 'query timeouts' ns1/named.stats >ns1/named.stats.timeouts-after || true
 mv ns1/named.stats ns1/named.stats-after
-diff ns1/named.stats.responses-before ns1/named.stats.responses-after >/dev/null || ret=1
-diff ns1/named.stats.rtt-before ns1/named.stats.rtt-after >/dev/null || ret=1
-diff ns1/named.stats.timeouts-before ns1/named.stats.timeouts-after >/dev/null && ret=1
+read before _ <ns1/named.stats.timeouts-before || true
+read after _ <ns1/named.stats.timeouts-after || true
+[ $((after - before)) -ge 3 ] || ret=1
 if [ $ret != 0 ]; then echo_i "failed"; fi
 status=$((status + ret))