Since the 1950s there has been continuing interest in the problem of joining the intermediate-time series solution for one-dimensional infiltration and the large time traveling wave solution. In practical field terms, however, observational errors, and errors produced by minor heterogeneities and nonuniformities of initial moisture content, will be far larger than the errors of even the crudest joining technique. The practical problem thus warrants only the minimum number of parameters and maximum simplicity. For soils which are initially relatively dry, two parameters suffice, and these are ideally taken as the physically meaningful and measurable sorptivity S and hydraulic conductivity K1. Polynomial fractions are unsuitable; piecewise representation is simple and adequate for most purposes, but a technique using the Knight infiltration solution of Burgers’ equation gives greater accuracy. It is well suited when a continuous representation and/or accuracy is desired.