  We study the distribution of energy level spacings in two models describing
coupled single-mode Bose-Einstein condensates. Both models have a fixed number
of degrees of freedom, which is small compared to the number of interaction
parameters, and is independent of the dimensionality of the Hilbert space. We
find that the distribution follows a universal Poisson form independent of the
choice of coupling parameters, which is indicative of the integrability of both
models. These results complement those for integrable lattice models where the
number of degrees of freedom increases with increasing dimensionality of the
Hilbert space. Finally, we also show that for one model the inclusion of an
additional interaction which breaks the integrability leads to a non-Poisson
distribution.
