I have a bike with grip shifters, and I just replaced the r derailleur. I think the indexing is correct, but it performs well only when upshifting. When downshifting to a larger cog, I consistently have to overshift a cog to get it to engage. Is this a grip shift issue or did I not properly adjust something on the derailleur?

What make of Grip shifter and derailleur? Was it doing the same before?

You need to adjust your cable length (use the adjuster) to balance up and down shifts. There is a bit of tweaking room to customize the performance to your desires.

in addition to what's already been mentioned, the cable in the housing may have too much friction somewhere.

i remember i once had a rear derailleur that needed a swift kick to go into the smallest cog.

+1
Some of the grip shifters on the lowest end bikes just never seem to work right in my experience. I never dealt with a NEW one though.

+2 on the cheap twisters. There are many different makes of index thumb or trigger shifters for little money that work well. And on most you can replace a cable in seconds. Just need to match gear make with shifter make when buying.

There's no mention of what type of derailleur the new one is. SRAM makes Grip Shift for both Shimano and SRAM pull ratios. If the replacement derailleur was "the other", that's likely the problem

Even within SRAM you can get messed up...I run a commuter MTB with tight, road bike-style gearing and bought a Rival short cage derailleur a few years ago. It was then that I discovered that SRAM's 1:1 and Exact Actuation are not the same thing. I had a similar problem as the OP - it'd shift well adjusted for either end, but not both.

I am traveling at the moment, but before I replaced the derailleur it was way out of adjustment. I swapped derailleurs so I could get 34t, was limited to 27 or 28 before. When I get back home I'll look at the grip shifters. I'm planning to do a drop bar conversion eventually so I didn't pay too much attention to what they are.

My experience w/GripShifters is similar to this. The lower-end are poor and need to be babied to work; the top-end ones I got for my "good" mtb are fine (though I still dislike installing new cables).

I'll second what's already been said regarding inexpensive trigger shifters out there - I recently tossed an old set of very worn GripShifts (400's, I think) and a worn LX rear derailleur, in favor of a set of SRAM X3 7-speed shifters (€25) and an SRAM X4 rear derailleur (€16.50). If you can spare the €50-ish, to me it's worth the change, removes a lot of headaches.

I like the concept of twist shifters, but they do seem to require a little more technique to use than trigger shifters -- especially old or cheap ones. I replaced the Sram SRT-400 grip shifters on my Trek 750 with some ST-EF51 mountain brifters and shifting is now very crisp and precise.

My wife's Trek 7100 has Sram 3.0 grip shifters with a Sram ESP 3.0 rear derailleur (what an X3 is today) and it actually works pretty well as a system. The left shifter, for the front derailleur, is semi-indexed, so it has a number of detents between the 1st, 2nd, and 3rd chain rings, which I like. I haven't used a twist shifter set, besides hers, that I really like. Maybe the 1:1 cable pull on the Sram derailleurs requires less of a twisting effort? Her bike has always shifted very smooth to me.