We propose a simple modification of lattice schemes reducing the bias of lattice option prices with respect to continuous time and state option prices. The modification is generic and is applied here to binomial and trinomial trees used to price American options. Unlike the typical lattice approaches which minimize the discrepancies between the approximating and target distributions by matching the first few moments of the distributions, we propose a lattice design targeting other objectives such as, for example, minimizing the distance between the computed and theoretical European price. This lattice is then used to price American options. We present a numerical study showing the benefits of the proposed modification in terms of speed and accuracy.