The mean square error efficiency of Grosenbaugh's (1964) adjusted 3P estimator is examined relative to four alternative estimators which use regression estimates of the conditional inclusion probabilities and true conditional inclusion probabilities. Actual mean square errors were calculated as the result of exhaustive sampling of populations that ranged in size from 9 elements to 144 elements and that exhibited widely different proportionality between the variable of interest and the auxiliary variable used for probability selection. The adjusted 3P estimator is as efficient or more efficient than all four competitors except when the unconditional probability of inclusion neared unity for some population elements. For. Sci. 33(3):617-631.