We consider maximum matchings in random bipartite graphs with a fixed degree distribution. This extends and simplifies work by Bohman and Frieze  and is motivated by a question of controllability of networks recently considered by Liu, Slotine, and Barabási . This is joint work with Paul Balister.  T. Bohman, A. Frieze, Karp-Sipser on random graphs with a fixed degree sequence, Combinatorics, Probability and Computing 20 (2011) pp. 721–741.  Y.-Y. Liu, J.-J. Slotine, A.-L. Barabási, Controllability of complex networks, Nature 473 (2011) pp. 167–173.