Recent lattice results strongly support the Axionic String Ansatz (ASA) for quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs as closed bosonic strings. The corresponding worldsheet theory is a deformation of the minimal Nambu-Goto theory. In order to understand better the ASA strings and as a first step towards a perturbative calculation of the glueball mass splittings we compare the ASA spectrum to the closed effective string theory. Namely, we model glueballs as excitations around the folded rotating rod solution with a large angular momentum J. The resulting spectrum agrees with the ASA in the regime of validity of the effective theory, i.e., in the vicinity of the leading Regge trajectory. In particular, closed effective string theory correctly predicts that only glueballs of even spin J show up at the leading Regge trajectory. Interestingly though, the closed effective string theory overestimates the number of glueball states far above the leading Regge trajectory.