Many people identify themselves as being either a “cat person” or a “dog person” based on their preference for these domestic animals. The purpose of this study was to test the common belief that there are personality differences between these types. Previous research has found differences between cat people and dog people on all Big Five personality traits, but studies comparing them on other personality characteristics have yielded mixed findings. Conjecturing that people prefer pets that complement their own personalities, we predicted that dog people should score higher than cat people on traits relating to dominance (i.e., social dominance orientation [SDO], interpersonal dominance, competitiveness, and narcissism). Two samples (ns = 506 and 503) were recruited online and completed these measures, as well as a question regarding their pet preferences. Findings for SDO and competitiveness were consistent with predictions in both studies, but no differences were found on interpersonal dominance or narcissism. The association of being a dog person with SDO and competitiveness persisted when gender differences in pet preference and personality were statistically controlled. We concluded that individuals who are high on these traits tend to prefer submissive pets such as dogs, whose temperament complements their preference for dominance.