Univariate stratification of survey populations with a generalization of the Lavallee-Hidiroglou method of stratum construction. The generalized method takes into account a discrepancy between the stratification variable and the survey variable. The determination of the optimal boundaries also incorporate, if desired, an anticipated non-response, a take-all stratum for large units, a take-none stratum for small units, and a certainty stratum to ensure that some specific units are in the sample. The well known cumulative root frequency rule of Dalenius and Hodges and the geometric rule of Gunning and Horgan are also implemented.