Research has examined the influence of a graduate student matching their advisor's demographic characteristics on a variety of outcomes, but comparatively few studies have examined students' preferences concerning such matching. Using data from a national survey of U.S. graduate students in five natural and social science disciplines, the analyses examine the importance students place on matching their advisor on three focal characteristics: gender, race, and religion. Overall, the analyses also find that the importance a student places on matching on one characteristic tends to be positively associated with the importance they place on matching on other characteristics. On gender-matching, the analyses find that female graduate students are more likely than male students to place importance on gender matching, but a majority still indicate that it is not at all important. However, a majority of Black students place importance on matching their advisor's race. Few students place any importance on religion matching, even among those who identify with a religion. While not discounting some groups' greater preference for matching their advisor's characteristics, these findings suggest that graduate programs should not assume that such preferences are universal or even particularly strong.