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Hybrid automatic repeat 1 request (HARQ) is a key enabler for ultrareliable communications. This paper optimizes transmit power for the initial transmission and the subsequent retransmissions of HARQ with either incremental redundancy or Chase combining, aiming to minimize the expected energy consumption given the target outage probability and the target latency. The main challenge is due to the fact that the outage probability is a complicated function of the power variables which are nested in successive convolutions. The existing works mostly use a classic upper bound to approximate the outage probability by assuming unbounded transmit power, then convert the original problem to a geometric programming (GP) problem. In contrast, we propose a novel and much tighter upper bound by taking the practical power limit into consideration. The new bound and the resulting new GP method are further extended to a broader group of channel models with various fading, multiple antennas, and multiple receivers. As shown in simulations, the GP method based on the new bound significantly outperforms the existing strategies that either fix transmit power or optimize power by the classic bounding technique.