  The redshift dependence of the abundance of collapsed objects places strong
constraints on cosmological models of structure formation. We apply a recently
proposed model describing the anisotropic collapse of inhomogeneous spatial
domains. Compared with the spherical top-hat model, this generic model leads to
significantly more collapsed objects at high redshifts: at redshift one and on
the scale of rich clusters a factor of 65. Furthermore, for a fixed
normalization of the initial fluctuation spectrum (\sigma_8=1), we predict four
times as much presently collapsed objects on the mass-scale of rich clusters
within the standard CDM cosmogony, compared to the spherical collapse.
