Opponents of the computational theory of mind (CTM) have held that the theory is devoid of explanatory content, since whatever computational procedures are said to account for our cognitive attributes will also be realized by a host of other `deviant' physical systems, such as buckets of water and possibly even stones. Such `triviality' claims rely on a simple mapping account (SMA) of physical implementation. Hence defenders of CTM traditionally attempt to block the trivialization critique by advocating additional constraints on the implementation relation. However, instead of attempting to `save' CTM by constraining the account of physical implementation, I argue that the general form of the triviality argument is invalid. I provide a counterexample scenario, and show that SMA is in fact consistent with empirically rich and theoretically plausible versions of CTM. This move requires rejection of the computational sufficiency thesis, which I argue is scientifically unjustified in any case. By shifting the `burden of explanatory force' away from the concept of physical implementation, and instead placing it on salient aspects of the target phenomenon to be explained, it's possible to retain a maximally liberal and unfettered view of physical implementation, and at the same time defuse the triviality arguments that have motivated defenders of CTM to impose various theory-laden constraints on SMA.