The Compact Ignition Tokamak (CIT) project, led by the Princeton Plasma Physics Laboratory, will employ a double null poloidal divertor as its primary means of energy and particle removal from the plasma. The fusion power handling capability of the divertor may represent the most severe constraint on the operating envelope for CIT. In addition to identifying this envelope based on divertor thermal performance, several studies aimed at improving this performance were examined. The reference divertor design concept employs small modules with pyrolytic graphite (PG) tiles. Studies of the sensitivity of the thermal performance of the passively cooled PG divertor design to separatrix sweeping parameters showed that a single pass sweep is near optimal for CIT conditions. An examination of the thermal performance of alternate materials found that some improvement (up to 20%) in the power handling capability of the divertor may be possible by using higher conductivity forms of PG, although the mechanical properties of these materials are not currently available. Alternate power handling approaches were examined and shown to have no significant improvement in thermal performance over the baseline passively cooled approach.