A distributed lag estimator is developed here from Bayesian priors regarding the"smoothness" of the lag curve. "Smoothness" priors of the dth degree are represented by a normal density function with zero mean of the difference of order d + 1 of the coefficients, where d will usually be one to zero. Such probabilistic priors, which do not imply any parametrization of the lag curve, are, it is contended here, a more accurate representation of the kind of prior knowledge that has led many researchers to use the polynomial distributed lag estimation procedure, and other parametrization procedures, in the past. The estimator developed here is, moreover, very simple in its implementation. All that is needed is any least squares regression program.