It is known that every complex of left R-modules has an exact cover. We con
sider the question of finding R for which every complex of left R-modules h
as an exact envelope. We first give a simple proof that for every R every c
omplex of left R-modules has a special exact preenvelope and then use this
to show that the left perfect rings are those R for which every complex has
an exact envelope. So, for example, this result holds for all artinian rin
gs.