This paper proposes means whereby a test for the goodness of fit and an estimate of the order of a Markov chain model may be obtained concurrently. Application of the method to daily precipitation data for two seasons of about 30 yr. in New Mexico, Colorado, and Oregon suggests two tentative conclusions. First, within a single climatic area, order estimates tend toward zero as precipitation events become rarer. This may occur at the drier stations or at higher thresholds defining a wet day. Second, between climatic areas, the station with the greater diversity of air mass types will tend to have order estimates greater than the station having the same seasonal mean precipitation but a less diverse climate.