  Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a
spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed
point spectrum X^{hG}. The E_2-term of the descent spectral sequence for
\pi_*(X^{hG}) cannot always be expressed as continuous cohomology. However, we
show that the E_2-term is always built out of a certain complex of spectra,
that, in the context of abelian groups, is used to compute the continuous
cochain cohomology of G with coefficients in lim_i M_i, where {M_i} is a tower
of discrete G-modules.
