Background Well-designed phase II trials must have acceptable error rates relative to a pre-specified success criterion, usually a statistically significant p-value. Such standard designs may not always suffice from a clinical perspective because clinical relevance may call for more. For example, proof-of-concept in phase II often requires not only statistical significance but also a sufficiently large effect estimate. Purpose We propose dual-criterion designs to complement statistical significance with clinical relevance, discuss their methodology, and illustrate their implementation in phase II. Methods Clinical relevance requires the effect estimate to pass a clinically motivated threshold (the decision value (DV)). In contrast to standard designs, the required effect estimate is an explicit design input, whereas study power is implicit. The sample size for a dual-criterion design needs careful considerations of the study's operating characteristics (type I error, power). Results Dual-criterion designs are discussed for a randomized controlled and a single-arm phase II trial, including decision criteria, sample size calculations, decisions under various data scenarios, and operating characteristics. The designs facilitate GO/NO-GO decisions due to their complementary statistical-clinical criterion. Limitations While conceptually simple, implementing a dual-criterion design needs care. The clinical DV must be elicited carefully in collaboration with clinicians, and understanding similarities and differences to a standard design is crucial. Conclusion To improve evidence-based decision-making, a formal yet transparent quantitative framework is important. Dual-criterion designs offer an appealing statistical-clinical compromise, which may be preferable to standard designs if evidence against the null hypothesis alone does not suffice for an efficacy claim.