There can be no successful limited war in Risk. Sure, two neighbors who don't particularly disagree in any meaningful way may occasionally trade a specific territory back and forth, but that hardly counts. What you really need to watch out for is those "limited" wars where you plan to get two or three terriories, maybe to clean up your border, maybe to get that extra army every turn. Sure, you'll attack, and you'll succeed, but when your opponent's turn comes around, they'll take back what you took, or some portion of it, and then you'll spend the next 2-3 turns figuring out where your border is. Meanwhile, that other guy took North America and is gunning for you with his eight armies per turn.

The only wars to fight in Risk are the ones you can win quickly and completely. Attack with overwhelming force; strike at the heart of your enemy's nation; destroy his ability to construct an army that can wear you down or distract you; and do it all in your initial attack or, at worst, the next turn's follow-up.

You don't need to destroy your enemy each time, but you do need to end the war. A small enemy may look in other directions to grow, but a nearly-big enemy will look to the small piece you've taken from them to become big again. Then you'll get bogged down and lose precious armies in a war of attrition every turn, while being robbed of the resources to attack on another front. Don't let yourself get caught there. Knock 'em out with the first punch.