Dispersion compensation was demonstrated with a highly dispersive waveguide consisting of two vertically coupled InGaAsP/InP asymmetric ridge waveguides with a large contrast between their refractive indices. A 3.3-ps positively chirped pulse was compressed-at a compression ratio of 62%--by the dispersion compensation produced by the dispersive waveguide. Moreover, experimental and theoretical investigations of dispersion compensation in this waveguide showed that the supermodes of the two coupled asymmetric waveguides play an important role in the observed pulse compression.