Human movements are variable, even in well-learned, controlled tasks of repeated movements. Simple models of repeated movements help us understand how the control of movements and the inherent noise in a system interact and influence the measurable variability in the outcome movements (the task). Here, we compare contemporary models for correcting repeated movements in the presence of noise, with a redundant goal (i.e. one that has many solutions) in the two dimensional task space. We show that the models share a similar structure, and explain their differences in noise processes. We compare simulations of model behavior to data from a previously published reaching task, to understand what features of the models we need in general. Ultimately, our simulations show that the correction or controller with free parameters in two independent directions is necessary to describe two-dimensional tasks in general. However, we cannot conclude in favor of one model over the other, because simulations also show that either of the different noise processes is sufficient.