  As currently implemented, single-photon sources cannot be made to produce
single photons with high probability, while simultaneously suppressing the
probability of yielding two or more photons. Because of this, single photon
sources cannot really produce single photons on demand. We describe a
multiplexed system that allows the probabilities of producing one and more
photons to be adjusted independently, enabling a much better approximation of a
source of single photons on demand. The scheme uses a heralded photon source
based on parametric downconversion, but by effectively breaking the trigger
detector area into multiple regions, we are able to extract more information
about a heralded photon than is possible with a conventional arrangement. This
scheme allows photons to be produced along with a quantitative
``certification'' that they are single photons. Some of the single-photon
certifications can be significantly better than what is possible with
conventional downconversion sources (using a unified trigger detector region),
as well as being better than faint laser sources. With such a source of more
tightly certified single photons, it should be possible to improve the maximum
secure bit rate possible over a quantum cryptographic link. We present an
analysis of the relative merits of this method over the conventional
arrangement.
