  Drummond had proposed four actions for Polchinski-Strominger effective string
theories at order $R^{-6}$, where $2\pi R$ is the length of the (closed) string
>. In \cite{covariant} it had been shown, based on covariance arguments, that
only two of them are independent. We analyse the spectral content of effective
string theories with these two actions. We show that the inclusion of these
actions does not yield corrections to the spectrum of Nambu-Goto theory
\cite{Arv}.
