We modify an algorithm of Bron and Kerbosch [1973] for maximal clique enumeration to choose more carefully the order in which the vertices are processed, giving us a fixed-parameter tractable algorithm with running time O (dn3d/3) on graphs with n vertices and degeneracy d. Our time bound matches a worst-case bound of (n− d) 3d/3 on the number of maximal cliques when d is a multiple of 3 and n≥ d+ 3. For graphs with degeneracy d and maximum clique size κ, the algorithm satisfies a time bound of O (d2n (d/κ) κ), and for Kh-minor-free graphs we obtain a time bound of n2O (hlog log h), matching a bound of Fomin et al.[2010] for the number of cliques in these graphs. We implement our algorithm and provide a comparative analysis of it and a different variation of the Bron–Kerbosch algorithm by Tomita et al.[2006] on a large corpus of real-world graphs with low degeneracy. Our algorithm always performs comparably with Tomita et al. on moderately sized graphs, in some cases is much faster, and due to its more space-efficient data structures is capable of being applied to significantly larger graphs.