  We present a number of second order maps, which pass the singularity
confinement test commonly used to identify integrable discrete systems, but
which nevertheless are non-integrable. As a more sensitive integrability test,
we propose the analysis of the complexity (``algebraic entropy'') of the map
using the growth of the degree of its iterates: integrability is associated
with polynomial growth while the generic growth is exponential for chaotic
systems.
