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We consider the optimization of power in incremental redundancy (IR) based hybrid automatic repeat request (HARQ) schemes when the maximum number of (re)transmissions is fixed. We formulate two optimization problems: (i) minimizing the packet drop probability (PDP) under a total average transmit power constraint, and (ii) minimizing the average transmit power under a fixed PDP constraint. We consider in detail the special case of only two allowed transmissions, and we prove that the two optimization problems are equivalent. For this special case, we also provide a sub-optimal root-finding solution and compare its performance with the optimal solution obtained through an exhaustive search. The results show that the optimal power allocation can provide significant gains over the equal power solution in terms of average transmit power spent. The performance of the proposed root-finding solution is practically the same as that of the optimal solution.