  The spectrum of glueballs in 2+1 dimensions is calculated within an extended
class of Isgur-Paton flux tube models and is compared to lattice calculations
of the low-lying SU(N) glueball mass spectra. Our modifications of the model
include a string curvature term and different ways of dealing with the flux
tube width. We find that the generic model is remarkably successful at
reproducing the positive charge conjugation, C=+, sector of the spectrum. The
only large (and robust) discrepancy involves the 0-+ state. This raises the
interesting possibility that the lattice spin identification is mistaken and
that this state is in fact 4-+. In addition, the Isgur-Paton model does not
incorporate any mechanism for splitting C=+ from C=- (in contrast to the case
in 3+1 dimensions), while the `observed' spectrum shows a substantial
splitting. We explore several modifications of the model in an attempt to
incorporate this physics in a natural way. At the qualitative level we find
that this constrains our choice to a picture in which the C=+/- splitting is
driven by mixing with new states built on closed loops of adjoint flux. However
a detailed numerical comparison suggests that a model incorporating an
additional direct mixing between loops of opposite orientation is likely to
work better; and that, in any case, a non-zero curvature term will be required.
We also point out that a characteristic of any string model of glueballs is
that the SU(N=infinity) mass spectrum will consist of multiple towers of states
that are scaled up copies of each other. To test this will require a lattice
mass spectrum that extends to somewhat larger masses than currently available.
