Won't Stay In Gear

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I have a 24 speed mountain bike and when I shift into 24th gear (biggest front gear and littlest back gear) and peddle hard the chain slips off from 24th gear and jumps into 21st gear and then back to 24th gear again. It constantly does this and makes 24th gear more trouble than it's worth. Any ideas what's doing this? I've played with the shifting cables and it doesn't seem to help any. Thanx.

well seems like some tuning should do the job.... or maybe loose cassete??

Try adjusting the H-screw on the rear derailleur. I forget which direction is which, but there is a maintenance section on www.parktool.com that goes through derailleur adjustments (among zillions of other things.)

Mrwarmachine, you can also try this link to some maintenance manuals online.

http://www.bikeforums.net/barnettes/

A worn chain is a common cause of poor shifting, but I would look at the H screw first.