What's the deal with compressionless brake cable housing?
I recently upgraded my brake cables with some Jagwire of the compressionless variety. jm2 is correct in saying the steel housing is reinforced with kevlar to prevent the longitudinal wires from buckling. The performance is very good and my brakes are far more responsive than with the old, traditional spiral-wound housing that was there before.

That said, installation is made a bit more tricky because:


The cable is not as flexy (it's a lot thicker than gear housing) so lengths must be cut appropriatly and secured well with the correct ferrules/end caps.
It is very difficult to cut. I tried first with a proper, full-size hack saw to get a smooth cut and it was immediately blunted. They must use very hard steel. I then just used some high-quality wire cutters which just about did the job and I smoothed up the cuts with a file. Make sure you have decent cutters if you're using compressionless.


It's also debatable whether compressionless is needed for brakes. It's needed for gears as they are indexed so need precise cable draw for a given shifter movement. Brakes have no such need, if you need more caliper movement just squeeze the lever a bit more. It probably gives some finer modulation but I reckon most of the improvements I experienced were just due to new cable vs 8-year-old ropey cable.