The optimization of queries in distributed database systems is known to be subject to delicate trade-offs. For example, the Mariposa database system allows users to specify a desired delay-cost tradeoff (that is, to supply a decreasing function u(d), specifying how much the user is willing to pay in order to receive the query results within time d); Mariposa divides a query graph into horizontal “strides,” analyzes each stride, and uses a greedy heuristic to find the “best” plan for all strides. We show that Mariposa's greedy heuristic can be arbitrarily far from the desired optimum. Applying a recent approach in multiobjective optimization algorithms to this problem, we show that the optimum cost-delay trade-off (Pareto) curve in Mariposa's framework can be approximated fast within any desired accuracy. We also present a polynomial algorithm for the general multiobjective query optimization problem, which approximates arbirarily well the optimum cost-delay tradeoff (without the restriction of Mariposa's heuristic stride subdivision).