For derivative securities that must be valued by numerical techniques, the trade-off between accuracy and computation time can be a severe limitation. For standard lattice methods, improvements are achievable by modifying the underlying structure of these lattices; however, convergence usually remains non-monotonic. In an alternative approach of general application, it is shown how to use standard methods, such as Cox, Ross, and Rubinstein (CRR), trinomial trees, or finite differences, to produce uniformly converging numerical results suitable for straightforward extrapolation. The concept of Λ, a normalized distance between the strike price and the node above, is introduced, which has wide ranging significance. Accuracy is improved enormously with computation times reduced, often by orders of magnitude.