The Buchen-Kelly density maximizes entropy among all risk-neutral densities that explain observed option prices for a fixed maturity. Since it is piecewise exponential, the inverse function of the associated distribution function is given in closed form. This makes Monte Carlo simulations from the Buchen-Kelly density extremely efficient via the classical inversion method. Unfortunately, however, the Buchen-Kelly density depends critically on the input option data and tends to be spiky, which is often not desired. We demonstrate how a deliberate choice of the input option data can resolve this issue and yield a smooth Buchen-Kelly density.