In this paper we consider all possible 1D and 2P cc̄ 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, cc̄ 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 cc̄ assignments are 1 3D3, 1 3D2, 1 1D2, 2 3P1 and 2 1P 1. A search for the mode J/ψπ0π0 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 1 3D2 and 1 1D2 states are predicted to have large (ca. 50%) radiative branching fractions to χ cIγ and hcγ, respectively. We predict that the 1 3D3 will also be relatively narrow and will have a significant (ca. 10%) branching fraction to χc2γ and should also be observable in B decay. Tests for non-cc̄ X(3872) assignments are also discussed.