The directional tuning profiles of motor cortical cells are commonly described by a cosine tuning function with three adjustable parameters (Georgopoulos, A.P., Kalaska. J.F., Crutcher, M.D., Caminiti, R., Massey, J.T., 1982. On the relations between the direction of two-dimensional (2D) arm movements and cell discharge in primate motor cortex. J. Neurosci. 2, 1527-1537). In this study the variation in the shape of the directional tuning profiles among a population of cells recorded from the arm area of the motor cortex of monkeys using movements in 20 directions, every 18 degrees, was examined systematically. This allowed the investigation of tuning functions with extra parameters to capture additional features of the tuning curve (i.e. tuning breadth, symmetry, and modality) and determine an 'optimal' tuning function. These functions provided better fit than the standard cosine one. The optimal function for the large majority of tuned cells was unimodal (84%), and only for a few of them (16%) it was bimodal. Of the unimodal cells, 73% exhibited symmetric and 27% asymmetric shape. The half-width, sigma, at the midpoint of optimal tuning curves differed among cells from 30 to 90 degrees, with a median at 56 degrees. This is much narrower than in the standard cosine tuning function with a fixed width of sigma = 90 degrees. It was concluded that motor cortical cells are more sharply tuned than previously thought.