Recently, Rim and Teply , using the notion of -exact modules, found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod of all unitary left -modules over an associative ring with identity. Some relations between -torsionfree and -exact covers have been investigated in . The purpose of this note is to show that if is Goldie’s torsion theory and is a precover class, then is a precover class whenever . Further, it is shown that is a cover class if and only if is of finite type and, in the case of non-singular rings, this is equivalent to the fact that is a cover class for all hereditary torsion theories .