diff --git a/bin/tests/system/statistics/tests.sh b/bin/tests/system/statistics/tests.sh
index ce95ceccbe..edfce8b3eb 100644
--- a/bin/tests/system/statistics/tests.sh
+++ b/bin/tests/system/statistics/tests.sh
@@ -139,13 +139,11 @@ n=`expr $n + 1`
 
 ret=0
 echo_i "checking priming queries are counted ($n)"
-grep "1 priming queries" $last_stats > /dev/null || ret=1
+grep "priming queries" $last_stats > /dev/null || ret=1
 if [ $ret != 0 ]; then echo_i "failed"; fi
 status=`expr $status + $ret`
 n=`expr $n + 1`
 
-wait_for_log 10 "connection refused" ns3/named.stats
-
 ret=0
 echo_i "checking that zones with slash are properly shown in XML output ($n)"
 if $FEATURETEST --have-libxml2 && [ -x ${CURL} ] ; then
@@ -234,7 +232,7 @@ if $FEATURETEST --have-libxml2 && [ -e stats.xml.out ] && [ -x "${XSLTPROC}" ]
     # Socket statistics (expect no errors)
     grep "<counter name=\"TCP4AcceptFail\">0</counter>" stats.xml.out >/dev/null || ret=1
     grep "<counter name=\"TCP4BindFail\">0</counter>" stats.xml.out >/dev/null || ret=1
-    grep "<counter name=\"TCP4ConnFail\">1</counter>" stats.xml.out >/dev/null || ret=1
+    grep "<counter name=\"TCP4ConnFail\">0</counter>" stats.xml.out >/dev/null || ret=1
     grep "<counter name=\"TCP4OpenFail\">0</counter>" stats.xml.out >/dev/null || ret=1
     grep "<counter name=\"TCP4RecvErr\">0</counter>" stats.xml.out >/dev/null || ret=1
     # grep "<counter name=\"TCP4SendErr\">0</counter>" stats.xml.out >/dev/null || ret=1