diff --git a/usr.sbin/newsyslog/newsyslog.c b/usr.sbin/newsyslog/newsyslog.c
--- a/usr.sbin/newsyslog/newsyslog.c
+++ b/usr.sbin/newsyslog/newsyslog.c
@@ -114,7 +114,8 @@
 #define	CE_PID2CMD	0x0400	/* Replace PID file with a shell command.*/
 #define	CE_PLAIN0	0x0800	/* Do not compress zero'th history file */
 #define	CE_RFC5424	0x1000	/* Use RFC5424 format rotation message */
-
+#define CE_NOEMPTY	0x2000	/* Do not rotate the file when its size */
+				/* is zero */
 #define	MIN_PID         5	/* Don't touch pids lower than this */
 #define	MAX_PID		99999	/* was lower, see /usr/include/sys/proc.h */
 
@@ -531,6 +532,11 @@
 			printf("does not exist, skipped%s.\n", temp_reason);
 		}
 	} else {
+		if (ent->flags & CE_NOEMPTY && ent->fsize == 0) {
+			if (verbose)
+				printf("--> Not rotating empty file\n");
+			return (free_or_keep);
+		}
 		if (ent->flags & CE_TRIMAT && !force && !rotatereq &&
 		    !oversized) {
 			diffsecs = ptimeget_diff(timenow, ent->trim_at);
@@ -1291,6 +1297,9 @@
 			case 'd':
 				working->flags |= CE_NODUMP;
 				break;
+			case 'e':
+				working->flags |= CE_NOEMPTY;
+				break;
 			case 'g':
 				working->flags |= CE_GLOB;
 				break;
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
@@ -21,7 +21,7 @@
 .\" the suitability of this software for any purpose.  It is
 .\" provided "as is" without express or implied warranty.
 .\"
-.Dd August 21, 2018
+.Dd February 26, 2021
 .Dt NEWSYSLOG.CONF 5
 .Os
 .Sh NAME
@@ -286,6 +286,18 @@
 This option would affect how the
 .Xr dump 8
 command treats the log file when making a file system backup.
+.It Cm E
+indicates that the log file should not be rotated when its
+size is zero.
+The
+.Cm E
+flag is mostly useful in conjunction with
+.Cm B
+flag to prevent
+.Xr newsyslog 8
+from inserting an informational 
+.Tn ASCII
+message into the new file.
 .It Cm G
 indicates that the specified
 .Ar logfile_name