According to the Head Start Act (1998), children are income-eligible for the program if their "families' incomes are below the poverty line." There are a number of statutory exceptions to this general rule and, according to the Head Start Bureau, the result is that about 6 percent of the children in the program are not poor. But the major national surveys of Head Start families report that 30 percent or more of Head Start children are not "poor." This paper confirms and explains the high proportion of nonpoor children in Head Start: at enrollment, at least 28 percent are not poor; at midyear, at least 32 percent are not poor; and by the end of the program year, at least 34 percent and perhaps more than 50 percent are not poor. Although the presence of some of these nonpoor children seems to be an appropriate or at least understandable aspect of running a national program with Head Start's current organizational structure, the presence of others seems much less warranted and raises substantial questions of horizontal equity. Moreover, taken together, the large number of nonpoor children suggests that the program is not well targeted to fulfill its mission of providing compensatory services to developmentally disadvantaged children--and reveals the essential ambiguity of Head Start's role in the wider world of early care and education. The income and program dynamics that have led to so many nonpoor children being in Head Start are also at work in many other programs, and, thus, our findings demonstrate the need to understand better how income eligibility is determined across various means-tested programs. (Contains 2 tables, 1 figure and 28 footnotes.)