When scholars extend their models and hypotheses to encompass additional cases, they commonly need to adapt their analytic categories to fit the new contexts. Giovanni Sartori's work on conceptual “traveling” and conceptual “stretching” provides helpful guidance in addressing this fundamental task of comparative analysis. Yet Sartori's framework draws upon what may be called classical categorization, which views the relation among categories in terms of a taxonomic hierarchy, with each category having clear boundaries and defining properties shared by all members. We examine the challenge to this framework presented by two types of nonclassical categories: family resemblances and radial categories. With such categories, the overly strict application of a classical framework can lead to abandoning to category prematurely or to modifying it inappropriately. We discuss solutions to these problems, using examples of how scholars have adapted their categories in comparative research on democracy and authoritarianism.