Compasses like that are usually anchored by double-sided tape and can be removed by pulling them up forcefully. Pliers help. If that doesn't work, you can break apart the base.

Making good small compasses appears to be quite difficult. The cheap keychain ones don't work very well and the nice NATO ones are very expensive. The issue may be that a small diameter needle simply can't produce much torque given the earth's weak magnetic field. So a bigger compass (say 1" diameter) works much better than a tiny one.

I have a Brunton GITD compass that cost $5 and is about 1.5" in diameter. It's not absolutely tiny but should fit in most kits. It would be marginal for an Altoid PSK and too big for a mini-Altoid kit, but ok for anything larger than those. It works much better than the little keychain and watchband compasses I've tried.

Over the years I have bought lots of cheap small button type compasses. After a while, about 80 percent develops a bubble or for one reason or another loses accuracy. There is one type manufactured by Recta that is perfect. I’ve got one for about fifteen years and it still works like a charm. I’ m talking about the Recta DW.

http://www2.recta.ch/FMPro?-db=recta_pro...1&-find

When you have trouble finding this type look for shops where they sell Victorinox SAK knifes. Victorinox puts the DMT and DM models in their survival pouches and you can also buy them separately. The three models are identical. This compass is sturdy and very reliable and already has a bubble when you buy it so you can use it as a level. The dial is “glow in the dark” and has a jewel bearing. They are quite cheap although I don’t know the exact price.

I've carried the same Suunto Clipper on the last two watches I owned -- that's over three years in city and in forest -- and no bubbles or problems.

For use in a kit the compass module snaps easily (and reversibly) out of the plastic housing. I also use the velcro strap that comes with the compass as a closing strap on Altoids tins.

Bear

Last year I bought two Suunto Clipper compasses (wich are identical to the Recta Clipper: I am not partial to a brand) and now they both have bubbles. The Recta DMT, DM, DW are just the best you can find in that size and for that prize.

Recta has excellent customer service, should it be needed.

I had to return my DS40 due to a bubble; they had it back to me in a couple of weeks. Not bad, considering it went from Tennessee (USA) to Switzerland & back.

David

There is a cool little compass from tru-nord from tad gear . I have the 200c I like it lot. http://www.tadgear.com/x-treme%20gear/compasses%20main/tru-nord.htm

PRECISION MILLED FROM SOLID 1.0625" BRASS ROD
DRY jeweled movement floats on a polished tapered pinnacle, and the brass ring is then threaded to the brass case making a watch-type seal
WATER AND SHOCK RESISTANT
LUMINOUS TIPPED DIAL
COMPASS = 1" DIAMETER X 0.4375" THICK
CLIP = 2"
Tru-Nord Compasses are compensated to provide a "Grid North"
MAY BE ADJUSTED FOR DIFFERENT REGIONS BY MAILING THEM BACK TO TRU-NORD FOR CALIBRATION
Lifetime Warranty
AVAILABLE IN BRASS OR BLACK FINISH