Colloidal quantum dots are attractive materials for efficient, low-cost and facile implementation of solution-processed optoelectronic devices. Despite impressive mobilities (1-30 cm2 V(-1) s(-1)) reported for new classes of quantum dot solids, it is--surprisingly--the much lower-mobility (10(-3)-10(-2) cm2 V(-1) s(-1)) solids that have produced the best photovoltaic performance. Here we show that it is not mobility, but instead the average spacing among recombination centres that governs the diffusion length of charges in today's quantum dot solids. In this regime, colloidal quantum dot films do not benefit from further improvements in charge carrier mobility. We develop a device model that accurately predicts the thickness dependence and diffusion length dependence of devices. Direct diffusion length measurements suggest the solid-state ligand exchange procedure as a potential origin of the detrimental recombination centres. We then present a novel avenue for in-solution passivation with tightly bound chlorothiols that retain passivation from solution to film, achieving an 8.5% power conversion efficiency.