diff --git a/makeself.sh b/makeself.sh
index a2d37ef..3b49aad 100755
--- a/makeself.sh
+++ b/makeself.sh
@@ -499,7 +499,10 @@ fi
 
 case $COMPRESS in
 gzip)
-    GZIP_CMD="gzip -c$COMPRESS_LEVEL"
+    # --no-name: omit the filename/timestamp from the gzip member
+    # header. Without it, the compressed output differ on every run even
+    # when the input is byte-for-byte identical.
+    GZIP_CMD="gzip --no-name -c$COMPRESS_LEVEL"
     GUNZIP_CMD="gzip -cd"
     ;;
 pigz) 
diff --git a/test/datetest b/test/datetest
index 8a83f2a..9c6f5df 100644
--- a/test/datetest
+++ b/test/datetest
@@ -94,10 +94,9 @@ testByteforbyte()
 {
   date='Sat Mar  3 19:35:21 EST 2016'
 
-  # bsdtar does not have option --mtime
-  # TODO: unstable test: first second differ: char 242, line 10
-
-  startSkipping
+  # GNU tar supports --tar-extra's --mtime option used below. 
+  # bsdtar (Mac/BSD) does not.
+  tar --version 2>/dev/null | grep -q GNU || startSkipping
 
   # Exercise
   ${SUT} --packaging-date "${date}" --tar-extra "--mtime 20160303" \