A practical problem in the rational design of a heterogeneous catalyst is to optimize its structure at all scales. By optimizing the large-pore network of a bimodal porous catalyst with a given nanoporosity (for example, zeolite or mesoporous catalyst) for the yield of diffusion-limited first-order reactions, it is found that catalysts typically benefit from a hierarchical pore network with a broad pore-size distribution. When comparing the performance of the optimal structures to that of self-similar, fractal-like pore hierarchies, it is found that the latter can be made to have the same effectiveness factor as the optimal ones, suggesting that fractal-like catalysts operate very near optimality, even if their structure is considerably different from that of the trite optima. This is useful, because fractal-like structures, have the advantage of being organized in a modular, natural way, potentially, easy to reproduce by templating. (C) 2004 American Institute of Chemical Engineers.