The Barut-Girardello states (the eigenstates of the SU(1, 1) lowering
generator K-) are considered in the harmonic oscillator Hilbert space.
They are found to have sub-Poissonian photon statistics. By using the
se states, the diagonal P-representation of the density operator is co
nstructed, and it is shown to be well behaved for non-classical photon
states.