Recent angle-resolved photoemission (ARPES) results for the insulating cuprate Sr 2 CuO 2 Cl 2 have provided experimental data that can be directly compared to the (theoretically) well-studied problem of a single hole propagating in an antiferromagnet. The ARPES results reported a small bandwidth, providing evidence for the existence of strong correlations in the cuprates. However, in the same experiment some discrepancies with the familiar two-dimensional t-J model were also observed. Here we discuss a comparison between the ARPES results and the quasiparticle dispersion of both (i) the t-t’-J Hamiltonian and (ii) the three-band Hubbard model in the strong-coupling limit. Both model Hamiltonians show that the experimentally observed one-hole band structure can be approximately reproduced using reasonable values for t’, or the direct oxygen hopping amplitude t pp.