State-of-the-art defenses against adversarial patch attacks can now achieve strong certifiable robustness with a marginal drop in model utility. However, this impressive performance typically comes at the cost of 10-100x more inference-time computation compared to undefended models -- the research community has witnessed an intense three-way trade-off between certifiable robustness, model utility, and computation efficiency. In this paper, we propose a defense framework named PatchCURE to approach this trade-off problem. PatchCURE provides sufficient "knobs" for tuning defense performance and allows us to build a family of defenses: the most robust PatchCURE instance can match the performance of any existing state-of-the-art defense (without efficiency considerations); the most efficient PatchCURE instance has similar inference efficiency as undefended models. Notably, PatchCURE achieves state-of-the-art robustness and utility performance across all different efficiency levels, e.g., 16-23% absolute clean accuracy and certified robust accuracy advantages over prior defenses when requiring computation efficiency to be close to undefended models. The family of PatchCURE defenses enables us to flexibly choose appropriate defenses to satisfy given computation and/or utility constraints in practice.