An optimal single-photon source should deterministically deliver one, and only one, photon at a time, with no trade-off between the source’s efficiency and the photon indistinguishability. However, all reported solid-state sources of indistinguishable single photons had to rely on polarization filtering, which reduced the efficiency by 50%, fundamentally limiting the scaling of photonic quantum technologies. Here, we overcome this long-standing challenge by coherently driving quantum dots deterministically coupled to polarization-selective Purcell microcavities. We present two examples: narrowband, elliptical micropillars and broadband, elliptical Bragg gratings. A polarization-orthogonal excitation–collection scheme is designed to minimize the polarization filtering loss under resonant excitation. We demonstrate a polarized single-photon efficiency of 0.60 ± 0.02 (0.56 ± 0.02), a single-photon purity of 0.975 ± 0.005 (0.991 ± 0.003) and an indistinguishability of 0.975 ± 0.006 (0.951 ± 0.005) for the micropillar (Bragg grating) device. Our work provides promising solutions for truly optimal single-photon sources combining near-unity indistinguishability and near-unity system efficiency simultaneously.