In this paper, we consider the possibility of obtaining a kernel machine that is sparse in feature space and smooth in output space. Smooth in output space implies that the underlying function is supposed to have continuous derivatives up to some order. Smoothness is achieved by applying a roughness penulty, a concept from the area of functional data analysis. Sparscness is taken care of by automatic relevance determination. Both are coinbined in u Bayesian inodel, which has been implemented and tested. Test results arc presented in the paper.