Among better-educated employed men, the fraction of full-time full-year (FTFY) workers is quite high and stable-around 90 percent-over time in the U.S. Among those with lower education levels, however, this fraction is much lower and considerably more volatile, moving within the range of 62-82 percent for high school dropouts and 75-88 percent for high school graduates. These observations suggest that the composition of unobserved skills may be subject to sharp movements within low-educated employed workers, while the scale of these movements is potentially much smaller within high-educated ones. The standard college-premium framework accounts for the observed shifts between education categories, but it cannot account for unobserved compositional changes within education categories. Our paper uses Heckman's two-step estimator on repeated Current Population Survey cross sections to calculate a relative supply series that corrects for unobserved compositional shifts due to selection into and out of the FTFY status. We find that the well-documented deceleration in the growth rate of relative supply of college-equivalent workers after mid-1980s becomes even more pronounced once we correct for selectivity. This casts further doubt on the relevance of the plain skill-biased technical change (SBTC) hypothesis. We conclude that what happens to the within-group unobserved skill composition for low-educated groups is critical for fully understanding the trends in the relative supply of college workers in the United States. We provide several interpretations to our selection-corrected estimates.