Query containment is the fundamental problem of deciding, given two database queries, if the result of the first query is always contained in the result of the second query. For a number of established query classes, an instance of this problem can be decided by computing a set of models of the first query, and then evaluating the second query on each of the models. We formalize this phenomenon by introducing the selfish models property; this property gives an avenue for establishing both the decidability of and complexity upper bounds for containment problems. Using this property, we show how existing results can be uniformly derived, and we present two significant novel positive results for first-order query containment problems, exhibiting complexity upper bounds for containment problems that were not previously known to be decidable.