The Principle of the Fixity of the Past (FP) holds that the past is ‘fixed’ in evaluating what we are free to do, and it is frequently invoked by incompatibilists when arguing that freedom and determinism are incompatible. However, several authors have argued that incompatibilists ought to abandon FP for a different principle, sometimes called the Principle of the Fixity of the Independent (FI). According to this principle, it is not the past in its entirety that is fixed, but only those parts of the past that are independent of our current choices. But a question remains: What about authors who are not friendly to incompatibilism in the first place? Is there any reason to think that compatibilists should also abandon their preferred interpretation of FP for something along the lines of FI? I examine perhaps the most influential version of (classical or leeway) compatibilism, David Lewis's ‘local‐miracle compatibilism’. I argue that although Lewis's version of local‐miracle compatibilism avoids being committed to anything like FI, his version faces a number of objections. Once we revise Lewis's version to avoid these objections, we arrive at a version of local‐miracle compatibilism that is committed to FI, or at least something very close.