A simple extension of the antisymmetrized product of strongly orthogonal geminals theory produces a “JK-only” one-matrix functional for the electron–electron repulsion energy of a closed-shell system that is exact for two-electron singlet ground states, size-extensive, and incorporates some intergeminal correlation and thus dispersion effects. The functional is defined only for one-matrices with occupation numbers that can be arranged into sets with elements that sum up to two. Its possible generalizations are discussed.