Evolving photonic quantum technologies and applications require higher and higher rates of single photon generation. In parallel, it is required that these generated photons are kept spectrally pure for multi-photon experiments and that multi-photon noise be kept to a minimum. In spontaneous parametric down-conversion sources, these requirements are conflicting, because spectral filtering to increase spectral purity always means lowering the rate at which photons are generated, and increasing the pump power means increasing the multi-photon noise. In this paper, we present a scheme, called extended heralding, which aims to mitigate the reduction of single-photon generation rate under spectral filtering by removing cases where we detect light in the rejection band of the heralding photons filter. Our experiment shows that this allows for higher single-photon generation rates with lower multi-photon noise than the standard approach of neglecting modes falling out of the filter bandwidth. We also show that by using active feed-forward control based on this extended heralding, it is possible to further improve the performance of the original source by physically eliminating uncorrelated photons from the output stream.