We investigate streamer formation in the troposphere, in electric fields above the breakdown threshold. With fully three-dimensional particle simulations, we study the combined effect of natural background ionization and of photo-ionization on the discharge morphology. In previous investigations based on deterministic fluid models without background ionization, so-called double-headed streamers emerged. But in our improved model, many electron avalanches start to grow at different locations. Eventually, the avalanches collectively screen the electric field in the interior of the discharge. This happens after what we call the “ionization screening time,” for which we give an analytical estimate. As this time is comparable to the streamer formation time, we conclude that isolated streamers are unlikely to exist in fields well above breakdown in atmospheric air.