The magnetic Compton profiles (MCPs) measured in the [100], [110], [111] and [112] directions in single-crystal nickel with an incident photon beam of energy 224 keV are presented and discussed. The momentum resolution achieved, of 0.43 atomic units, improves on previous studies by almost a factor of two, and facilitates the interpretation of the MCPs in terms of the underlying spin-dependent momentum densities. Calculations have been performed using the linear muffin-tin orbital method, within both the local spin-density approximation (LSDA) and the generalized gradient approximation (GGA). Comparison with experiment reveals the limitations of the LSDA at low momentum, where the GGA is better able to reproduce the contribution of the s-and p-like electrons. All of the calculations overestimate the moment associated with the d-like electrons, for momenta corresponding to the first Brillouin zone. We also confirm the existence of the so-called Umklapp shoulders, which derive from the Fermi surface topology.