  The class of loop spaces whose mod p cohomology is Noetherian is much larger
than the class of p-compact groups (for which the mod p cohomology is required
to be finite). It contains Eilenberg-Mac Lane spaces such as the infinite
complex projective space and 3-connected covers of compact Lie groups. We study
the cohomology of the classifying space BX of such an object and prove it is as
small as expected, that is, comparable to that of BCP^\infty. We also show that
BX differs basically from the classifying space of a p-compact group in a
single homotopy group. This applies in particular to 4-connected covers of
classifying spaces of Lie groups and sheds new light on how the cohomology of
such an object looks like.
