In this paper we consider all possible 1D and 2P ccbar assignments for the recently discovered X(3872). Taking the experimental mass as input, we give numerical results for the E1 radiative widths as well as the three principal types of strong decays; open-charm, ccbar annihilation and closed-charm hadronic transitions. We find that many assignments may be immediately eliminated due to the small observed total width. The remaining viable ccbar assignments are 3D3, 3D2, 1D2, 2 3P1 and 2 1P1. A search for the mode J/psi pi0 pi0 can establish the C-parity of the X(3872), which will eliminate many of these possibilities. Radiative transitions can then be used to test the remaining assignments, as they populate characteristic final states. The 3D2 and 1D2 states are predicted to have large (ca.50%) radiative branching fractions to chi_1 gamma and h_c gamma respectively. We predict that the 3D3 will also be relatively narrow and will have a significant (ca.10%) branching fraction to chi_2 gamma, and should also be observable in B decay. Tests for non-ccbar X(3872) assignments are also discussed.
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