The attainability of the Hashin-Shtrikman bounds by a class of sequentially laminated composites with prescribed and generally different volume fractions of the core laminates at each rank is well-known. It is demonstrated that in the limit of a rank-infinity laminate these bounds are attained by choosing identical volume fractions for the core laminates. (C) 2002 Elsevier Science B.V. All rights reserved.