The recently investigated $\ell \mathrm{asso}$ model predictive control (MPC) is applied to the terminal phase of a spacecraft rendezvous and capture mission. The interaction between the cost function and the treatment of minimum impulse bit (MIB) is also investigated. The propellant consumption with $\ell \mathrm{asso}$ MPC for the considered scenario is noticeably less than with a conventional quadratic cost and control actions are sparser in time. Propellant consumption and sparsity are competitive with those achieved using a zone-based $\ell 1$ cost function, whilst requiring fewer decision variables in the optimisation problem than the latter. The $\ell \mathrm{asso}$ MPC is demonstrated to meet tighter specifications on control precision, and also avoids the risk of undesirable behaviours often associated with pure $\ell 1$ stage costs.