The counterfactual account of physical computation is simple and, for the most part, very attractive. However, it is usually thought to trivialize the notion of physical computation insofar as it implies ‘limited pancomputationalism’, this being the doctrine that every deterministic physical system computes some function. Should we bite the bullet and accept limited pancomputationalism, or reject the counterfactual account as untenable? Jack Copeland would have us do neither of the above. He attempts to thread a path between the two horns of the dilemma by buttressing the counterfactual account with extra conditions intended to block certain classes of deterministic physical systems from qualifying as physical computers. His theory is called the ‘algorithm execution account’. Here we show that the algorithm execution account entails limited pancomputationalism, despite Copeland’s argument to the contrary. We suggest, partly on this basis, that the counterfactual account should be accepted as it stands, pancomputationalist warts and all.