This paper develops algorithms for listing and estimation of all subsets in a finite distributed lag model, with a view to select the best subset from the listed subsets thereby removing the parameters that contribute insignificantly to the model and more so reduce the problem of multi-collinearity. We describe the method of estimation for full and subset finite distributed lag models. In order to select the best order for full and subset finite distributed lag models, Akaike information criterion (AIC) is adopted. The estimation technique is illustrated with respect to a meteorological series where rainfall is the dependent variable and temperature is the explanatory variable. The best order for the full finite distributed lag model is achieved at lag six (6) and the 2q-1 for all subsets gave a total of sixty three (63) subsets that is 26-1. The best order having estimated the sixty three equations occurred at the 31st subsets. This led to the removal of insignificant parameters in the subset model. The subset model is more appropriate as the value for the AIC in the subset model is less than the AIC value in the full model. Apart from the intercept, the full finite distributed lag model had six parameters while the subset model had three parameters meaning that those parameters that contributed insignificantly to the model have been removed thereby leading to a better model and a reduction in the problem of multi-collinearity.