New power allocation schemes taking both sum-rate and fairness into account for MIMO downlink communications employing successive zero-forcing dirty paper coding are presented in this letter. Specifically, using a revised ℓ1-norm fairness measure that allows for a more comprehensive consideration when users have an unequal number of receive antennas, the optimal tradeoff between sum-rate and fairness for MIMO downlink communications with arbitrary channel statistics is completely characterized. A novel stochastic power allocation scheme capable of achieving this optimal tradeoff is also given. To put the optimal tradeoff into practical use, an explicit rule for selecting operating sum-rate from the tradeoff is then proposed. Simulation results show that the new scheme can yield higher sum-rate and better fairness at the same time.