We consider the λ-(µ−) and λ-(µ-) dimensions of modules taken under a cotorsion theory (F , C) satisfying the Hereditary Condition, and establish some inequalities between the dimensions of the modules of a short exact sequence, not necessarily Hom (F , −) exact. We investigate the question of whether the property of having a (special) F -or C-resolution of length n is resolving, closed under extensions or coresolving and establish some inequalities connecting the λ-(µ−) and λ-(µ-) dimensions of modules in a short exact sequence.