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We demonstrate a single-photon source based on a quantum dot in a micropost microcavity that exhibits a large Purcell factor together with a small multiphoton probability. For a quantum dot on resonance with the cavity, the spontaneous emission rate is increased by a factor of 5, while the probability to emit two or more photons in the same pulse is reduced to 2% compared to a Poisson-distributed source of the same intensity. In addition to the small multiphoton probability, such a strong Purcell effect is important in a single-photon source for improving the photon outcoupling efficiency and the single-photon generation rate, and for bringing the emitted photon pulses closer to the Fourier transform limit. © 2003 American Institute of Physics.