Properties of states bound by potentials with positive Laplacian

States of two-body systems bound by a spherically symmetric potential whose Laplacian is positive are considered. Constraints are derived on the kinetic energies and radii of states with the lowest energy for a given angular momentum, which improve on previous results of the author. These constraints become relatively very tight at high angular momentum. Inequalities are also derived between the energies of states of differing angular momentum and particle mass.