As an alternative, Edgeworth binomial trees allow for an analyst-specified skew and kurtosis in spot price returns; see Edgeworth series. This approach is useful when the underlying's behavior departs (markedly) from normality. A related use is to calibrate the tree to the volatility smile (or surface), by a "judicious choice" of parameter values—priced here, options with differing strikes will return differing implied volatilities. For pricing American options, an Edgeworth-generated ending distribution may be combined with an R-IBT. This approach is limited as to the set of skewness and kurtosis pairs for which valid distributions are available. The more recent Johnson binomial trees