Great question — answering as the UphillTech team:
Shimano's revoshift is a bit cantankerous. Okay - its a very budget system intended for bikes whose total lifespan is under 1000 km. As such, it has minimal resistance to wear internally. It sounds like your inner cable has stretched a little, and/or some of the guides have wear. This adds up to a little more slack in the wire. Check your rear derailleur for a barrel adjuster, and there might be another one at the shifter or on the frame, but those last two are less likely. Try backing out the screw a quarter of a turn and see if that makes an improvement. This effectively makes the outer longer, accommodating for the slight increase in the inner cable length. You could go up to a full...
Full answer by Criggie: https://bicycles.stackexchange.com/a/96634 (CC BY-SA 4.0).
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