  Lewin and Lieb have recently proven several new bounds on the
exchange-correlation energy that complement the Lieb-Oxford bound. We test
these bounds for atoms, for slowly-varying gases, and for Hooke's atom, finding
them usually less strict than the Lieb-Oxford bound. However, we also show
that, if a generalized gradient approximation (GGA) is to guarantee
satisfaction of the new bounds for all densities, new restrictions on the the
exchange-correlation enhancement factor are implied.
