Most measurements of racial and ethnic segregation, particularly comparative analyses across cities, have relied on the Index of Dissimilarity ("D"). Recently, however, it has been demonstrated that cities with different racial compositions also have different expected values of "D" under a random distribution of whites and blacks. Here "D" is compared with another, increasingly used, segregation index which we call "S". Applied to measurement of school segregation, "S" equals the proportional underrepresentation of black students in the school attended by the average white student in the district. A principal value of "S" is that its expected value is independent of racial composition and rapidly approaches zero, even for modest-sized units of analysis. Also, "S" can be"decomposed" into segregation within subsets of entities and segregation between subsets. The behavior of "S" and "D" are explored with data on segregation in higher education and segregation of workers across different places of employment. (Author)