Abstract. This paper presents a refined and constructive version of the commutant lifting theorem (see [Sz.-NF3]) which includes the Treil--Volberg generalization of that theorem (see [TV]). This theory is used to solve a new variant of the Sarason interpolation problem.

AMS Subject Classification (1991): 47A57, 47A45

Received April 13, 1999. (Registered under 2710/2009.)