The exchange stiffness (A(ex)) is one of the key parameters controlling magnetization reversal in magnetic materials. We used a method based on the spin spiral formation in two ferromagnetic films antiferromagnetically coupled across a non-magnetic spacer layer and Brillouin scattering to measure A(ex) for a series of Co1-delta X delta (X=Cr, Ni, Ru, Pd, Pt) thin film alloys. The results show that A(ex) of Co alloys does not necessarily scale with M-s; A(ex) approximately decreases at the rate of 1.1%, 1.5%, 2.1%, 3.5%, and 5.6%, while M-s decreases at the rate of 1.1%, 0.5%, 1.1%, 3.7%, and 2.5% per addition of 1 at% of Pt, Ni, Pd, Cr, and Ru, respectively.