A great way to carry a fairly large amount of cordage with minimal bulk is as follows: use 3 or 4 fingers of your off hand as a "spool" to wrap the cordage around. Once you've got what you feel is a proper amount of cordage, use the free end to wrap around the bundle (after taking it off your fingers). This gives you a cordage bundle that looks the way mountain climbers stow their rops, but by not having any kind of spool in the middle of the cordage, and wrapping it tightly, you can get a surprising amount of cordage put into a kit this way.
To make the cordage bundle even more versatile, you can then wrap snare wire around the cordage, and then finish it all off with a few wraps of duct tape. So in a bundle that's about 3x1 inches, you can easily get 30 feet of 165lb breaking strain twine, 15 or 20 feet of USGI tripwire for use as snare wire, and likely about 3 to 5 feet of duct tape. Such a bundle easily fits across the top of an Altoids tin, leaving most of the tin free for other goodies.
I've never spent much time learning to make cordage, so I always make sure to have plenty of it on-hand, since cordage is such an integral part of outdoors survival.