The first thing I would check is the roundness of your wheel. If you jack it up you can either use a dial-indicator (more money solution) or a chunk of bailing wire (less money solution). Since people with a dial-indicator know how to use them (normally) I'll discuss the wire method.
You need to take a piece of wire (maybe a foot long) and wrap it around your fork tube or swingarm (depending on the wheel) so that the tip is almost touching the side of the rim. If you watch that gap and spin the wheel you can tell if you have any side to side wobble in the rim (called run-out). If that is the case you will want a blue tire crayon (because I'm going to teach you how to fix it). Next you need to move the wire to the inside of the rim (outside if you want to take the tire off and look like a semi-pro) and check for out of round. If both checks show no out of true condition you can tighten carefully, checking frequently to make sure you're not making things worse. If things are out of true, you need to make sure you haven't bent the rim (every wobble should have an opposite wobble on the other side of the rim). To true the wheel, spin the wheel holding your tire crayon just off the rim. Keep moving the crayon in until you make contact with part of the wheel (the mark indicates where your rim is too close to the crayon). Do the same thing on the other side. You will normally find the opposite out of true 180 degrees on the wheel. You can tighten spokes that pull opposite of the crayon marks. Remember every action has an opposite reaction (not equal in every case Einstein). Same with out of round conditions except you mark the inside of the rim and tighten where there is no crayon mark (because it's too far from the axle). Work slowly. If the rim is bent, you're going to have to buy a new rim.
"My KLR belongs to God, when he wants it clean he washes it."