Over the past 40 years, an irrelevance proposition has been prevalent in law-and-economics scholarship: bargaining power should affect only price and not non-price terms of a contract. In contrast, practitioners and commentators in industry regularly invoke bargaining power to explain static and dynamic variance in non-price contract terms. This paper unpacks and analyzes the assumptions of the strong- and weak-versions of this bargaining power irrelevance proposition, to bridge the gap between theory and the real world. In the first half of the paper, we identify and discuss a variety of explanations for the effect of bargaining power on contract design, under conditions of information asymmetry and positive transaction costs. These include the effects of shifts in market supply and demand and the effect of bargaining through lawyers. In the second half of the paper, we present an in-depth examination of one set of explanations, concerning the impact of bargaining power and information asymmetry on non-price terms, when the value and cost of non-price terms vary across contracting parties. In the extreme cases in which one or the other party enjoys overwhelming bargaining power, the efforts of that party to capture a larger share of the surplus by screening or signaling may compromise the efficiency of the non-price terms. We show that this incentive disappears or is mitigated when bargaining power is more evenly shared between the parties: for example, when a monopolist faces the threat of competition, when the parties can renegotiate, or when they engage in bilateral bargaining with more even bargaining power. As a whole, the paper provides a theoretical basis for interpreting the intuition among market participants that the impact of bargaining power extends beyond price terms. Before concluding, we briefly suggest implications for legal policy, particularly the contract law doctrine of unconscionability.