  We apply a `dimensional reduction' mechanism to the evaluation of the
functional integral for the vacuum energy of a real scalar field in the
presence of non-trivial backgrounds, in d+1 dimensions. The reduction is
implemented by applying a generalized version of Gelfand-Yaglom's theorem to
the corresponding functional determinant. The main outcome of that procedure is
an alternative representation for the Casimir energy, which involves one
spatial dimension less than the original problem. We show that, for some
configurations, important information about the reduced problem can be
obtained. We also show that the reduced problem allows for the introduction of
an approximation scheme which is novel within this context.
