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TPS610981: Most efficient boost chip for bluetooth low energy

Part Number: TPS610981
Other Parts Discussed in Thread: TLV61225, TPS61098,

I'm looking at the TPS610985X family of chips and am having some trouble figuring out which is best to use. My average load current is about 20 uA, peak current is 10 mA. I'm running my board off of a single AA battery and would like to keep it running as long as possible (down to a dead battery), so somewhere in the 0.7 to 0.8 voltage range would be nice. Since my input voltage is so low, I don't need the LDO so can disable that for extra energy savings. Which chip in the TPS610985X family would be best for this scenario? I already tried the TLV61225, but it seemed to have much too high of a current draw at low input voltage levels.