  We compare numerical evolutions performed with the BSSNOK formulation and a
conformal decomposition of a Z4-like formulation of General Relativity. The
important difference between the two formulations is that the Z4 formulation
has a propagating Hamiltonian constraint, whereas BSSNOK has a zero-speed
characteristic variable in the constraint subsystem. In spherical symmetry we
evolve both puncture and neutron star initial data. We demonstrate that the
propagating nature of the Z4 constraints leads to results that compare
favorably with BSSNOK evolutions, especially when matter is present in the
spacetime. From the point of view of implementation the new system is a simple
modification of BSSNOK.
