  The singularity confinement test is very useful for isolating integrable
cases of discrete-time dynamical systems, but it does not provide a sufficient
criterion for integrability. Quite recently a new property of the bilinear
equations appearing in discrete soliton theory has been noticed: the iterates
of such equations are Laurent polynomials in the initial data. A large class of
non-integrable mappings of the plane are presented which both possess this
Laurent property and have confined singularities.
