  We introduce a set of consistency conditions on the S-matrix of theories of
massless particles of arbitrary spin in four-dimensional Minkowski space-time.
We find that in most cases the constraints, derived from the conditions, can
only be satisfied if the S-matrix is trivial. Our conditions apply to theories
where four-particle scattering amplitudes can be obtained from three-particle
ones via a recent technique called BCFW construction. We call theories in this
class constructible. We propose a program for performing a systematic search of
constructible theories that can have non-trivial S-matrices. As illustrations,
we provide simple proofs of already known facts like the impossibility of spin
$s > 2$ non-trivial S-matrices, the impossibility of several spin 2 interacting
particles and the uniqueness of a theory with spin 2 and spin 3/2 particles.
