After fitting a set of parallel-push Shimano V brakes to my tourer, I discovered that the front wheel is offset to the left a couple mm. I had been using cantis and fenders until then and this flaw (my mistake) had remained completely unnoticed since this has produced no effect on handling or brake pad wear.
To correct, this should I start from scratch and redo the wheel or is it possible to center the rim by undoing tension on one side and tightening the spokes on the other? Or should I leave it alone? Thanks.

First confirm that it is the wheel, and not something else. Off center front wheels are fairly rare, but it does happen. There are two easy ways to confirm whether the wheel is built on center (rim centered between the axle faces).

1-loosen the brakes so they're out of the way. Stand bike on level ground, open the QR, jiggle the fork a bit to make sure it's settled fully on the axle and close the QR. Note the side and distance of any off center in the fork. Remove and flip the wheel and repeat. If the side reversed and the distance is about the same, then the wheel is off center. If it stayed to the same side and distance than the wheel is fine, and the error is in the fork. (it could also be other things, but the wheel is likely OK).

2- build a tabletop dishing gauge. Arrange 3 identical glasses or soup cans in a triangle on your table. Place rim on these (tire off for accuracy), and stack coins up to the acle face. Flip wheel and note whether axle rose, fell or stayed at the same height (same height is a pass, moved is a fail).

Then, to answer your original question. If the wheel is off center but otherise OK, you can move the rim to center by alternately tightening and loosening spokes. I prefer not to alternate because dyslexia might kick in, so I loosen all the spokes on one side 1/2 turn, then tighten the opposite side the same amount. You can also combine this with a general tightening if you wish by only tightening one side, or loosening less than you tighten or some variant of the loosen/tighten amounts.

Before you do anything, do this simple test. With the bike upright on the floor, release the quick-release, make sure the forks are sitting solely on the axle and re-tighten. Measure the distance from the rim to left brake pad, or better the left fork blade. Now turn the wheel around and do the same, also to the feft. Are these measurements the same (within an mm or so? Yes? Wheel is dished correctly. Don't change it. No? Loosening the spokes on one side and tightening the other will be appropriate, but be aware that you will also have to mess with further truing when you do this. (Not in theory, but nearly always in practice.)

If the answer was no, the wheel isn't the issue. Either the fork blades are not symmetrical around the steerer centerline or the dropouts are not located at exactly the same height. In either case, you can file the top of the dropout to correct the brake situation, but if the fork blades are off, you now have a front wheel that does not sit in the plane of the rest of the bike.

Be careful here: A non steel fork should be left as-is if it is the blades and dropouts filed with real care. A second visual opinion from someone in the industry is strongly advised, both for the alignment and wisdom of filing. Steel forks that are not lightweight steel are a lot more forgiving. Still, keep in mind how hard you are going to be on this fork. Are you heavy? An equipment beater? Ride things into the ground? Adjust that brake the best you can and forget it. Impact testing helmets is best left to the pros.

Ben

FB, that was fun. We independently came up with the identical quick test! I think this guy is on good hands!

Ben

I will usually tighten one side to correct the problem. If 1/4 turn doesn't do it then loosen the other side 1/4 turn.

only disc front wheels are actually dished, purposely, then its not by much..

If the wheel is properly tensioned it's better practice to loosen one side first, then tighten the other.

!/4 turn won't make or break it unless the wheel is over tensioned.

Sure, but keep in mind that tightening one side also tightens the other side, which is how it should be. My point though is that you end up with a higher tension wheel than you started with. If that is still in bounds, fine.

That's not the point. For one thing 1/4 turn on a well tensioned wheel may not move it very far, because you are increasing overall tension, and therefore the resistance to lateral changes. Secondly, if you tension first the spokes will be harder to turn, especially as you reach the end of the process, which makes it more likely that you will round off spoke nipples. If the tension is on the low end of acceptable I can see combining tension and dish - it's something mechanics do often. Otherwise as I said it's better practice to loosen one side and then tighten the other.

clayface, excuse me if it sounds a bit belittled, but did you make sure the cone shaped coils in each side of the skewers are pointing with their nerrow side towards the wheel? I've seen quite a few bikes with one of the coils positioned the other way around, thus making the wheel tilted to one side of the fork.

FB,
WHat coins should be used?Quarters,dimes, nickels or penny's??

I use 10 Peso coins since they stack the best. You can also use poker chips. For those who want maximum precision, use a new ream of paper and remove sheets to the exact height. That will allow you to work to a tolerance of ±.001".

Paper is .003"