The thickness of copolymer layers adsorbed to track-etched mica pores was measured as a function of the molecular weight of the polymer when N(A)/N(B) < 0.2, where N(A) and N(B) are the number of monomers in the adsorbing and solvated blocks, respectively. Two polymers were studied : poly(2-vinylpyridine)/polystyrene, PVP/PS, and poly(methacrylic acid)/poly(butyl methacrylate), PMAA/PBMA. The adsorbing blocks were PVP and PMAA, and N(A) was constant for each copolymer series. The copolymers were adsorbed from dilute solution in a selective solvent so that the driving force for adsorption appeared to be primarily a lyophobic effect. The equivalent hydrodynamic thickness (L(H)) of a layer was determined from the measured reduction in pressure-driven flow of polymer-free solvent after adsorption of a copolymer. The data for both series of copolymers are correlated by L(H)/a almost-equal-to N-B(0.26), where a is the Stokes-Einstein radius of the solvated block and the prefactor depends on the monomer of the solvated block.