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The aim of this study was to compare the demand for food under concurrent progressive- and fixed-ratio schedules. Twelve brushtail possums participated in 16 conditions where schedule, progression and food type were varied. An incrementing schedule increased the fixed-ratio requirement within and across sessions and was arranged as either a geometric sequence (base 2), or an arithmetic sequence (step 5). Two foods were tested: a flaked barley and coco-pop(®) mix versus rolled oats. Overall, performance was similar for most possums in the within- and across-session incrementing schedules. An analysis of the estimates of essential value and break point produced the same account of demand for foods under the geometric or arithmetic progressions and within- and across-session procedures for 8 of 12 possums. Six possums showed higher demand for rolled oats compared to flaked barley, and two possums showed higher demand for flaked barley compared to rolled oats. Incrementing ratios within, rather than between sessions using an arithmetic progression was demonstrated to be a time efficient procedure for investigating demand for different food types without affecting conclusions about the relative demand for those foods.