One of the most compact, packable gun cleaning kits I've run across at a reasonable price that has a rifle-length cleaning rod is the Hoppe's Univeral Field Cleaning Kit. For under thirty bucks, this kit has a six-piece rifle-or-shotgun-length aluminum cleaning rod, some Hoppe's Lubricating Oil, a can of Hoppe's 9 Bore Cleaner, a variety of cleaning patches, patch holders, a shotgun adapter, and a handy nylon case with Velcro closures that's about five inches, by six inches and barely an inch-and-a-half thick when closed up.
There's a pocket with a Velcro closure sewn in the lower flap of the case and a pocket sewn in behind the bore cleaner, oil, and cleaning rod stretch loops. You can keep the cleaning patches in one pocket and the rod ends an accessories in the other pocket. One area lackin' for this kit is that no bore brushes or jags were included, so you'll have to supply or purchase those separately.
It never fails when you're out shooting that eventually you'll get a stuck case, bullet, or other situation where a BoreSnake or cable just won't work. With a full-length cleaning rod taken apart and stowed in the case, It will easily slip into your range bag or even a pocket in your cargo pants or backpack.... or even into the top pocket of a Ruger 10/22 Take-Down Rifle bag. Besides, my gal's used to my Hoppe's 9 cologne after all these years.
So if you're lookin' for a handy little cleaning kit... you might want to take a look at this little kit from a name that's been around for quite some time... Hoppe's Universal Field Cleaning Kit