In 2 experiments, the authors examined whether and to what degree young adults can learn to produce random planar motion of the index finger or fingers. Three different types of information feedback were provided to the participants (N = 8 in each experiment) over up to 5 days of practice across the 2 experiments. The results from both experiments revealed that the participants produced a relatively low level of movement randomness in finger motion and that they did not learn through practice to enhance the stochastic properties of their movement under any feedback conditions. The findings provide further evidence that there are relatively tight constraints on the number of dimensions that are regulating single-limb planar motion and that those constraints are not susceptible to change through typical learning protocols.