Kernel estimates of discrete probabilities are considered, with emphasis on computation of the smoothing parameters. Different approaches based on minimum mean squared error, cross-validation and pseudo-Bayesian techniques are compared, particularly from the points of view of reliability and ease of computation. The advantages of a fractional allocation procedure and of computing the bandwidths marginally for each variable are pointed out. Multicategory variables and incomplete data can be coped with. The relationship between the kernel method and other smoothing techniques for categorical data is discussed.