A micromechanical dislocation model of frictional slip between two asperities is presented. The model suggests that when the contact radius is smaller than a critical value, the friction stress is constant, of the order of the theoretical shear strength, in agreement with reported atomic force microscope (AFM) friction experiments. However, at the critical value there is a transition beyond which the friction stress decreases with increasing area, until it reaches the second transition where the friction stress gradually becomes independent of the contact size. This is in contrast to previous theories, which assume that the friction stress is always independent of the size. The present model also predicts that the mechanisms of slip are size dependent. Before the first transition, the constant friction stress is associated with concurrent slip without the aid of dislocation motion. The first transition corresponds to the minimum contact size at which a single dislocation loop is nucleated and sweeps through the whole contact interface, resulting in a single–dislocation–assisted (SDA) slip. This mechanism is predicted to prevail for a wide range of contact sizes, from 10 nm to 10 µm in radius for typical dry adhesive contacts; however, there are no available experimental data in this size range. The second transition is found to be caused by the effective Peierls stress which stabilizes the dislocation loop within the contact region, resulting in dislocation pile–ups. Beyond the second transition, slip is assisted by cooperative glide of dislocations in the pile–up. For sufficiently large contacts the mechanism of cooperative glide induces a size–independent friction stress, in agreement with observations in surface force apparatus (SFA) friction experiments. This paper (Part I) addresses the first transition: from concurrent slip to SDA slip. The second transition is analysed in a companion paper (Part II).