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The use of the cum- f rule to define stratum endpoints is widespread. Dalenius and Hodges (1959) show that for a fixed number of strata, cum- f rule endpoints result in lower expansion-estimator variance than alternative endpoints if (1) the variable of interest is both the stratification and allocation variable, (2) the stratification variable is approximately uniformly distributed between adjacent endpoints, and (3) Neyman allocation is used. We investigate two procedures that have been suggested when one or more of these conditions do not hold. Singh (1971) proposes a model-assisted modification to the cum- f rule when an auxiliary variable is the stratification variable. We evaluate Singh's procedure for the cases of allocation based on the auxiliary data and for model-assisted allocation (Dayal, 1985). For skewed populations, Lavallee and Hidiroglou (1988) have developed an iterative algorithm for assigning optimal endpoints for one certainty and several non-certainty strata. We propose and evaluate a model-assisted modification to the Lavallee and Hidiroglou algorithm when the input to the algorithm is auxiliary data instead of the survey variable of interest.