  Spontaneous parametric down-conversion is a common source of quantum photonic
states that is a key enabling quantum technology. We show that the source
characteristics can be optimized by adjusting the beam waists of the pump mode
and the signal and idler collection modes. It is possible to obtain
simultaneously near unity heralding efficiency and single-photon purity using a
bulk crystal with both metrics approaching $\approx0.98$ under appropriate
conditions. Importantly, our approach can be applied over a wide range of pump,
signal, and idler wavelengths without requiring special crystal dispersion
characteristics. As an example, we obtain a heralding efficiency of 0.98, a
single-photon purity of 0.98, and a pair production rate of 10.9
pairs/(s$\textrm{ }$mW) using a 450-$\mu$m-long $\beta$-barium borate crystal
pumped by a 405-nm-wavelength laser and nearly degenerate signal and idler
wavelengths around 810 nm. Here, the pump mode has a waist of 310 $\mu$m and
the signal and idler collection modes have a waist of 145.4 $\mu$m, which can
be produced straightforwardly using standard laboratory components. Our work
paves the way for realizing a simple approach to producing quantum photonic
states with high purity and heralding efficiency.
