We study spin transport in lateral spin valves with constricted channels. Using electromigration, we modulate the spin accumulation by continuously varying the width of the non-magnetic (NM) channel at a single location. By fitting the non-local spin signal data as a function of the NM channel resistance, we extract all the relevant parameters regarding spin transport from a single device. Simulations show that constricting the channel blocks the diffusion of the accumulated spins rather than causing spin flipping. This result could be used to improve the design of future spintronic devices devoted to information processing.