A comparison was made between paired-stimulus and multiple-stimulus without-replacement preference assessments with the common brushtail possum (Trichosurus vulpecula). Both assessments identified similar preferences in foods by individual possums. A progressive-ratio reinforcer assessment showed that all foods identified in the preference assessments functioned as reinforcers when presented in a single-schedule arrangement, including those foods identified as low-preference. In a concurrent-schedule arrangement, the food type that was generally shown as being of high-preference at higher schedule requirements during the single-schedule assessment, was shown to have higher measures of preference again. It was also found that when the concurrent alternative was on a fixed-ratio 50 schedule, the impact upon preference was less than when the concurrent alternative was on a fixed-ratio 20. We concluded that preference is relative to the other alternatives available, and stimuli identified as low-preference when assessed through paired stimulus or multiple stimulus without replacement methods may still be appropriate to use as reinforcers to maintain operant responding.