The knowledge of the spin diffusion length, λA, is a prerequisite for the estimation of the spin Hall angle of given materials. We investigate the spin-current absorption of materials with a short λA using AuW stripes inserted in Cu-based lateral spin valves. Width variations of the AuW stripe lead to drastic changes of the spin absorption which cannot be explained by a conventional analysis. We show that the spin-current polarization and the spin-accumulation attenuation in Cu in the vicinity of the spin absorber must be precisely taken into account for an accurate estimation of λA. We propose an analytical extension of the standard diffusion model of spin transport and spin absorption based on the existence of an effective spin diffusion length for Cu being in direct contact with AuW. The calculations are supported by numerical investigations which allow us to extract proper values of λA.