Hi Graham!
A good question, and one I hope to answer for myself. Cork tape just isn't cutting it for me, and my hands are sore. It's not bad for fast road-riding, but mountainous, rough single-track is beating up my hands something terrible.
In the past, I've had really good luck by first installing a quality, dense closed-cell padding like Grab-On and then compression-wrapping it to half-thickness using a nice, padded vinyl-skinned tape. Unfortunately, such nice tape seems rarely available; cork has taken over the market.
An alternative I have been considering is one of a variety of gel under-tape pads, but from "used" ones I've seen when friends retaped, the gel pads seem to have squashed out flat where the pressure is greatest.
Frankly, I don't look forward to the task of upgrading my handlebar coverings, what with cable housings for the bar-end shifters, the brake levers, and the interrupter levers. Still, it has to be done at some point. When it does, I may well go back to the compression-wrapped Grab-Ons. They might work well again even if all I can find to use as an over-wrap is something "corkish".
Does anyone know if a product called "Gatorskin" 'bar tape is still available? I used some by that name years ago, and it lasted a very long time indeed (decades).
Best,
Dan.