High coincidence-to-accidental ratio (CAR) is crucial for photon-pair sources (PPSs) integrated with pump reject filters (PRFs) in silicon, but CAR values currently reported for integrated PPS/PRF chips still fall short of those achieved using stand-alone sources with external PRFs. Here we report measured and modelled CAR values for a micro-ring resonator PPS integrated with a PRF consisting of a three-stage, cascaded (via their through ports), contra-directional coupler (CDC) that compare favorably even with some stand-alone sources. CDC-based PRFs provide the benefits of compact area and wide reject bands without a need for tuning, in comparison to prior-art implementations.