We analyze published cosmogenic 3He depth profiles through the till that covers relict glacier ice in Beacon Valley, Antarctica, in order to derive rigorous constraints on the till thickness history, and on the amount and rate of ice loss by sublimation. The till is a residue of debris-laden ice that sublimed. The 3He profiles show that the lower 80% of the till formed in the past 310–43 k.y. under sublimation rates averaging >7 m·m.y.−1 (meters per million years). Such rapid recent growth of the till contradicts previous interpretations that it is older than 8.1 Ma at an adjacent site, where it encloses volcanic ash of this age. We question whether the ash provides a valid age constraint for the ice. Cosmogenic nuclide analysis of the till where the ash was collected for dating should resolve this question.