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According to the fundamental theorems of welfare economics, any competitive equilibrium is Pareto efficient. Unfortunately, competitive equilibrium prices only exist under strong assumptions such as perfectly divisible goods and convex preferences. In many real-world markets, participants have non-convex preferences and the allocation problem needs to consider complex constraints. Electricity markets are a prime example, but similar problems appear in many real-world markets, which has led to a growing literature in market design. Power markets use heuristic pricing rules based on the dual of a relaxed allocation problem today. With increasing levels of renewables, these rules have come under scrutiny as they lead to high out-of-market side-payments to some participants and to inadequate congestion signals. We show that existing pricing heuristics optimize specific design goals that can be conflicting. The trade-offs can be substantial, and we establish that the design of pricing rules is fundamentally a multi-objective optimization problem addressing different incentives. In addition to traditional multi-objective optimization techniques using weighing of individual objectives, we introduce a novel parameter-free pricing rule that minimizes incentives for market participants to deviate locally. Our theoretical and experimental findings show how the new pricing rule capitalizes on the upsides of existing pricing rules under scrutiny today. It leads to prices that incur low make-whole payments while providing adequate congestion signals and low lost opportunity costs. Our suggested pricing rule does not require weighing of objectives, it is computationally scalable, and balances trade-offs in a principled manner, addressing an important policy issue in electricity markets.