  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.
