We demonstrate a method that likely will improve the accuracy of functionals used in density functional theory and pair density functional theory. In deriving the method we show that the coupling-integrated exchange-correlation hole used in density functional theory obeys all the N-representability conditions as non-integrated holes and we give two such conditions, not normally used by the density functional theory community. We will also show that in addition to the normal adiabatic connection there exist a dual adiabatic connection where the kinetic energy is integrated over the inverse electron mass. (C) 2009 Elsevier B.V. All rights reserved.