  Heralded single photon sources are often implemented using spontaneous
parametric downconversion, but their quality can be restricted by optical loss,
double pair emission and detector dark counts. Here, we show that the
performance of such sources can be improved using cascaded downconversion, by
providing a second trigger signal to herald the presence of a single photon,
thereby reducing the effects of detector dark counts. We find that for a setup
with fixed detectors, an improved heralded second-order correlation function
$g^{(2)}$ can always be achieved with cascaded downconversion given sufficient
efficiency for the second downconversion, even for equal single-photon
production rates. Furthermore, the minimal $g^{(2)}$ value is unchanged for a
large range in pump beam intensity. These results are interesting for
applications where achieving low, stable values of $g^{(2)}$ is of primary
importance.
