  Much recent attention has focused on theories with large extra compactified
dimensions. However, while the phenomenological implications of the volume
moduli associated with such compactifications are well understood, relatively
little attention has been devoted to the shape moduli. In this paper, we show
that the shape moduli have a dramatic effect on the corresponding Kaluza-Klein
spectra: they change the mass gap, induce level crossings, and can even be used
to interpolate between theories with different numbers of compactified
dimensions. Furthermore, we show that in certain cases it is possible to
maintain the ratio between the higher-dimensional and four-dimensional Planck
scales while simultaneously increasing the Kaluza-Klein graviton mass gap by an
arbitrarily large factor. This mechanism can therefore be used to alleviate (or
perhaps even eliminate) many of the experimental bounds on theories with large
extra spacetime dimensions.
