  The evolution pattern of level crossings and exceptional points is studied in
a non-integrable pairing model with two different integrable limits. One of the
integrable limits has two independent parameter-dependent integrals of motion.
We demonstrate, and illustrate in our model, that quantum integrability of a
system with more than one parameter-dependent integral of motion is always
signaled by level crossings of a complex-extended Hamiltonian. We also find
that integrability implies a reduced number of exceptional points. Both
properties could uniquely characterize quantum integrability in small Hilbert
spaces.
