diff --git a/share/man/man5/periodic.conf.5 b/share/man/man5/periodic.conf.5
--- a/share/man/man5/periodic.conf.5
+++ b/share/man/man5/periodic.conf.5
@@ -365,7 +365,7 @@
 .Pq Vt bool
 Set to
 .Dq Li YES
-if you want to rotate your daily accounting files.
+if you want to rotate your daily process accounting files.
 No rotations are necessary unless
 .Va accounting_enable
 is enabled in
diff --git a/usr.sbin/newsyslog/newsyslog.conf.5 b/usr.sbin/newsyslog/newsyslog.conf.5
--- a/usr.sbin/newsyslog/newsyslog.conf.5
+++ b/usr.sbin/newsyslog/newsyslog.conf.5
@@ -403,6 +403,7 @@
 .Xr bzip2 1 ,
 .Xr gzip 1 ,
 .Xr xz 1 ,
+.Xr zstd 1 ,
 .Xr syslog 3 ,
 .Xr chown 8 ,
 .Xr newsyslog 8 ,
diff --git a/usr.sbin/periodic/etc/daily/460.status-mail-rejects b/usr.sbin/periodic/etc/daily/460.status-mail-rejects
--- a/usr.sbin/periodic/etc/daily/460.status-mail-rejects
+++ b/usr.sbin/periodic/etc/daily/460.status-mail-rejects
@@ -52,6 +52,12 @@
 		    elif [ -f /var/log/maillog.$n.bz2 ]
 		    then
 			bzcat -fc /var/log/maillog.$n.bz2
+		    elif [ -f /var/log/maillog.$n.xz ]
+		    then
+			xzcat -f /var/log/maillog.$n.xz
+		    elif [ -f /var/log/maillog.$n.zst ]
+		    then
+			zstdcat -fc /var/log/maillog.$n.zst
 		    fi
 		    n=$(($n - 1))
 		done
diff --git a/usr.sbin/periodic/etc/monthly/200.accounting b/usr.sbin/periodic/etc/monthly/200.accounting
--- a/usr.sbin/periodic/etc/monthly/200.accounting
+++ b/usr.sbin/periodic/etc/monthly/200.accounting
@@ -18,16 +18,30 @@
 	W=/var/log/utx.log
 	rc=0
 	remove=NO
+	filetoread=$W.0
 	if [ ! -f $W.0 ]
 	then
-	    if [ -f $W.0.gz ]
+	    if [ -f $W.0.gz ] || [ -f $W.0.bz2 ] || [ -f $W.0.xz ] || [ -f $W.0.zst ]
 	    then
+	        TMP=`mktemp -t accounting`
 		remove=YES
-		zcat $W.0.gz > $W.0 || rc=1
-	    elif [ -f $W.0.bz2 ]
-	    then
-		remove=YES
-		bzcat $W.0.bz2 > $W.0 || rc=1
+		filetoread=$TMP
+		if [ -f $W.0.gz ]
+		then
+		    zcat $W.0.gz > $TMP || rc=1
+		elif [ -f $W.0.bz2 ]
+		then
+		    bzcat $W.0.bz2 > $TMP || rc=1
+		elif [ -f $W.0.xz ]
+		then
+		    xzcat $W.0.xz > $TMP || rc=1
+		elif [ -f $W.0.zst ]
+		then
+		    zstdcat $W.0.zst > $TMP || rc=1
+		else
+		# shouldn't get here, unless something disappeared under us.
+		    rc=2
+		fi
 	    else
 		echo '$monthly_accounting_enable is set but' \
 		    "$W.0 doesn't exist"
@@ -39,10 +53,10 @@
 	    echo ""
 	    echo "Doing login accounting:"
 
-	    rc=$(ac -p -w $W.0 | sort -nr -k 2 | tee /dev/stderr | wc -l)
+	    rc=$(ac -p -w $filetoread | sort -nr -k 2 | tee /dev/stderr | wc -l)
 	    [ $rc -gt 0 ] && rc=1
 	fi
-	[ $remove = YES ] && rm -f $W.0;;
+	[ $remove = YES ] && rm -f $TMP;;
 
     *)  rc=0;;
 esac
diff --git a/usr.sbin/periodic/etc/security/800.loginfail b/usr.sbin/periodic/etc/security/800.loginfail
--- a/usr.sbin/periodic/etc/security/800.loginfail
+++ b/usr.sbin/periodic/etc/security/800.loginfail
@@ -53,6 +53,8 @@
 		case $f in
 		    *.gz)	zcat -f $f;;
 		    *.bz2)	bzcat -f $f;;
+		    *.xz)	xzcat -f $f;;
+		    *.zst)	zstdcat -f $f;;
 		esac
 	    done
 	[ -f ${LOG}/auth.log ] && cat $LOG/auth.log
diff --git a/usr.sbin/periodic/etc/security/900.tcpwrap b/usr.sbin/periodic/etc/security/900.tcpwrap
--- a/usr.sbin/periodic/etc/security/900.tcpwrap
+++ b/usr.sbin/periodic/etc/security/900.tcpwrap
@@ -53,6 +53,8 @@
 		case $f in
 		    *.gz)	zcat -f $f;;
 		    *.bz2)	bzcat -f $f;;
+		    *.xz)	xzcat -f $f;;
+		    *.zst)	zstdcat -f $f;;
 		esac
 	    done
 	[ -f ${LOG}/messages ] && cat $LOG/messages