  Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can
be obtained as a direct limit of finitely generated maximal CM modules. We
point out two consequences of this characterization: (1) Every balanced big CM
module, in the sense of Hochster, can be written as a direct limit of small CM
modules. In analogy with Govorov and Lazard's characterization of flat modules
as direct limits of finitely generated free modules, one can view this as a
"structure theorem" for balanced big CM modules. (2) Every finitely generated
module has a preenvelope with respect to the class of finitely generated
maximal CM modules. This result is, in some sense, dual to the existence of
maximal CM approximations, which is proved by Auslander and Buchweitz.
