  We compute semi-classical corrections to the energy of rotating closed
Nambu-Goto strings. We confirm the results obtained by means of the
Polchinski-Strominger action. We also show that in this semi-classical
approximation, the spectrum of physical excitations contains modes that are
unphysical non-perturbatively, i.e., to which no physical excitations of the
covariantly quantized Nambu-Goto string correspond.
