Originally Posted by cny-bikeman

You say it "seems true" but also say there is a 3mm side-to-side difference. It's on or the other. The rim could be physically bent or it could be you just are not using proper truing technique. Is there a bike co-op near you? In-person help is usually best. if not Google "true bike wheel" and study written guides first (Parktool.com and Sheldonbrown.com are generally well-regarded). Check out videos if you wish, but many are incomplete or inaccurate.