There has been some recent interest in 'generalized' density functional theories, in which the fundamental variable is the density of electron pairs (pair density), instead of the electron density. Much of the work along these lines has focused on Weisacker-type functionals of the density and has not explicitly considered the N-representability problem. As is discussed here, such theories cannot be accurate. Some new functionals for the kinetic energy, which may address the problem, are proposed, and the correlation component is discussed as a relatively small correction to the Kohn-Sham kinetic energy. (c) 2005 Elsevier B.V. All rights reserved.