Bright sources of indistinguishable single photons are strongly needed for the scalability of quantum information processing. Semiconductor quantum dots are promising systems to build such sources. Several works demonstrated emission of indistinguishable photons while others proposed various approaches to efficiently collect them. Here we combine both properties and report on the fabrication of ultrabright sources of indistinguishable single photons, thanks to deterministic positioning of single quantum dots in well-designed pillar cavities. Brightness as high as 0.79±0.08 collected photon per pulse is demonstrated. The indistinguishability of the photons is investigated as a function of the source brightness and the excitation conditions. We show that a two-laser excitation scheme allows reducing the fluctuations of the quantum dot electrostatic environment under high pumping conditions. With this method, we obtain 82±10% indistinguishability for a brightness as large as 0.65±0.06 collected photon per pulse.