For two electron atoms the ground-state wavefunctions of the form psi(r(1),r(2)) = phi(r(1))phi(r(2))(cosh ar(1) + cosh ar(2))(1 + 0.5r(12)e(-br12)) where n and r(2) are the coordinates of two electrons and r(12) = vertical bar r(1) - r(2)vertical bar, is made accurate by optimizing a, b and phi(r). This is done by solving a variationally derived equation for phi(r) and optimizing a and b to minimize [H). This wavefunction gives accurate energies and other properties of these systems. (C) 2015 Elsevier B.V. All rights reserved.