  The first UV sources in the universe are expected to have coupled the HI spin
temperature to the gas kinetic temperature via scattering in the Lyman-alpha
resonance [the Wouthuysen-Field (WF) effect]. By establishing an HI spin
temperature different from the temperature of the CMB, the WF effect should
allow observations of HI during the reionization epoch in the redshifted 21 cm
line. This paper investigates four mechanisms that can affect the strength of
the WF effect that were not previously considered: (1) Photons redshifting into
the HI Lyman resonances may excite an H atom and result in a radiative cascade
terminating in two-photon 2s->1s emission, rather than always degrading to
Lyman-alpha as usually assumed. (2) The fine structure of the Lyman-alpha
resonance alters the photon frequency distribution and leads to a suppression
of the scattering rate. (3) The spin-flip scatterings change the frequency of
the photon and cause the photon spectrum to relax not to the kinetic
temperature of the gas but to a temperature between the kinetic and spin
temperatures, effectively reducing the strength of the Wouthuysen-Field
coupling. (4) Near line centre, a photon can change its frequency by several
times the line width in a single scattering event, thus potentially
invalidating the usual calculation of the Lyman-alpha spectral distortion based
on the diffusion approximation. It is shown that (1) suppresses the WF coupling
strength by a factor of up to ~2, while (2) and (3) are important only at low
kinetic temperatures. Effect (4) has a <=3% effect for kinetic temperatures
T_k>=2K. If the pre-reionization IGM was efficiently heated by X-rays, only
effect (1) is important. Fitting formulae are provided for the range of T_k>=2K
and Gunn-Peterson optical depth 10^5--10^7. [ABRIDGED]
