  We study the effect of a prolonged epoch of reionization on the angular power
spectrum of the Cosmic Microwave Background. Typically reionization studies
assume a sudden phase transition, with the intergalactic gas moving from a
fully neutral to a fully ionized state at a fixed redshift. Such models are at
odds, however, with detailed investigations of reionization, which favor a more
extended transition. We have modified the code CMBFAST to allow the treatment
of more realistic reionization histories and applied it to data obtained from
numerical simulations of reionization. We show that the prompt reionization
assumed by CMBFAST in its original form heavily contaminates any constraint
derived on the reionization redshift. We find, however, that prompt
reionization models give a reasonable estimate of the epoch at which the mean
cosmic ionization fraction was ~50%, and provide a very good measure of the
overall Thomson optical depth. The overall differences in the temperature
(polarization) angular power spectra between prompt and extended models with
equal optical depths are less than 1% (10%).
