We consider the optimal transmission power control of a single wireless node with stochastic energy harvesting and an infinite/saturated queue with the objective of maximizing a certain reward function, e.g., the total data rate. We develop simple control policies that achieve near optimal performance in the finite-horizon case with finite energy storage. The same policies are shown to be asymptotically optimal in the infinite-horizon case for sufficiently large energy storage. Such policies are typically difficult to directly obtain using a Markov Decision Process (MDP) formulation or through a dynamic programming framework due to the computational complexity. We relate our results to those obtained in the unsaturated regime, and highlight a type of threshold-based policies that is universally optimal.