Most efficient way to convert from 3.5-4.2V (singe cell LiPo) to stable 3.3V for currents up to 500 mA?

This question is hypothetical - there is no specific project, I just have an obsession with efficiency.

I use a lot of 3.3V modules, and have a bunch of single-cell LiPo batteries (which are amazing), so I'm wondering what would be the best way to combine the two if I were to make a project that would need to maximize battery usage efficiency. As far as I know, there are two options:

1. Low dropout linear regulator (LDO) - not easy to find one with a dropout of 0.2V at 500 mA loads, but the bigger problem is that linear regulators turn the extra voltage into heat, making them very inefficient.
2. Use a boost converter to bring that LiPo voltage to 5V, and then use a switching regulator to bring it down to 3.3V. I haven't found any modules on Ebay or Aliexpress that would do it with combined efficiency above 90%, unfortunately. And it appears that the switching regulators are very inefficient at low current draws, typical ones dropping down to 60% at 50 mA and below.

Are there any other ways? Is it possible to achieve an efficiency of at least 95% for such a small voltage difference?

• 4.2 - 4.0V has relatively small energy. Accept energy loss if linear. Then linear worst case is 3.3/4 = 83.5% at 4V, increasing to 3,3.3.5 ~= 94% at 3.5V. So mean is say 3.3/3.75 = 88%. An LDO with 0.2v dropout is doable. If desired a MOSFET + comparator will allow essentially any dropout desired (almost :-) ). For 0.2V at 500 mA R=V/I =0.2/0.5 = 0.4 Ohm = a very mediocre FET. ie almost an MOSFET willa give the desired dropout. || Best performance would be a buck converter with synchronous dual MOSFET output switch. Efficiencies over 90% should be achievable for most or all of the range. Commented Sep 17, 2019 at 11:23
• Welcome to EE.SE! Keep in mind that questions about optimization (i.e., "What is the best ...?") require a definition about what problem dimensions are to be optimized for your application, such as size, speed, energy consumption, user experience, etc. Since these can't be optimized all at once, you need to have a good idea of which ones are most important to you, and be able to articulate that clearly to us. Commented Sep 17, 2019 at 16:28