A paper by the same authors entitled "Estimation of the parameters of a linear functional relation" investigated the large sample properties. It appeared in the Journal of the Royal Statistical Society, Series B. 1961. In the present paper small sample behavior of several slope estimators is compared on the basisof bias and mean square error. When replicated observations are made the estimators considered all have approximately the same mean square error but the bias enables us to choose among them when we have partial information concerning the parameters. When there is no replication of observations and the errors are suitably restricted there exists a class of consistent estimators which are ratios of linear forms in the observations. There are rational grounds for choosing a member of the class when partial information is available concerning the spacing of the true values of one of the variables.