In this paper we return to the problem of adsorption of correlated random copolymers at a liquid-liquid interface. We explain our particular interest in the exponentially decaying sequential correlations, which are obtained by a specially developed "coloring" procedure. In comparison with our previous work [N. A. Denesyuk and I. Y. Erukhimovich, J. Chem. Phys. 113, 3894 (2000)], we present an improved analytical analysis, based on the full Green functions of the chains under consideration. Calculating the interfacial tension enables us to introduce a new definition of the adsorption point and to compare it with that applied within the ground state dominance approximation. Bearing in mind the possible practical applications, we additionally consider the case of diblock copolymer. We show that, for equal selectivities and mean compositions, adsorption is always deeper for the chains of diblock copolymers. Nevertheless, for a wide range of identified parameters correlated random copolymers can still serve as effective compatibilizers, comparable with diblock copolymers and polyblock chains. (C) 2001 American Institute of Physics.