  We show, by explicit calculation, that the next correction to the universal
Luescher term in the effective string theories of Polchinski and Strominger is
also universal. We find that to this order in inverse string-length, the
ground-state energy as well as the excited-state energies are the same as those
given by the Nambu-Goto string theory, the difference being that while the
Nambu-Goto theory is inconsistent outside the critical dimension, the
Polchinski-Strominger theory is by construction consistent for any space-time
dimension. Our calculation explicitly avoids the use of any field redefinitions
as they bring in many other issues that are likely to obscure the main points.
