The conventional analysis of a Peltier cooler approximates the material properties as independent of temperature using a constant properties model (CPM). Alternative concepts have been published by Bian and Shakouri (2006 Appl. Phys. Lett. 89 212101), Bian (et al 2007 Phys. Rev. B 75 245208) and Snyder et al (2012 Phys. Rev. B 86 045202). While Snyder's Thomson cooler concept results from a consideration of compatibility, the method of Bian et al focuses on the redistribution of heat. Thus, both approaches are based on different principles. In this paper we compare the new concepts to CPM and we reconsider the limit for maximum cooling. The results provide a new perspective on maximum cooling.