Helium and hydrogen recombination lines observed in low-metallicity, extragalactic H II regions provide the data used to infer the primordial helium mass fraction, Y_P. The ionization corrections for unseen neutral helium (or hydrogen) are usually assumed to be absent; i.e., the ionization correction factor is taken to be unity (icf = 1). In this paper we revisit the question of the icf for H II regions ionized by clusters of young, hot, metal-poor stars. Our key result is that for the H II regions used in the determination of Y_P, there is a ``reverse ionization correction: icf < 1. We explore the effect on the icf of more realistic inhomogeneous H II region models and find that for those regions ionized by young stars, with ``hard radiation spectra, the icf is reduced further below unity. In Monte Carlos using H II region data from the literature (Izotov and Thuan 1998) we estimate a reduction in the published value of Y_P of order 0.003, which is roughly twice as large as the quoted statistical error in the Y_P determination.
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