We study the formation of interstellar molecular lines in a turbulent velocity field with finite correlation length, extending previous work to the ultraviolet absorption bands of the A1 II X1 + system of CO. Our results show clearly that a finite correlation length strongly affects the shape of the saturated absorption lines. This in turn leads to ambiguous physical parameters if observed line profiles are analysed on the basis of classical theory. Using a homogeneous plane-parallel model, we apply our theory to the highresolution observations by Sheffer et al. of the A -x (5, 0) and (6, 0) bands of CO towards Oph and deduce the following parameters: Nco =9.5 X 1014 cm 2, ncol= 1.36 x1014 , the ratio of turbulent and thermal velocities J/Vtherm =4.0, and the isotopic ratio Nl2co!NI3co 70. An estimated slab thickness of L -2 pc implies a correlation length 1-0.3 pc. Key words: line: formation - line: profiles - ISM: molecules - ultraviolet: ISM.