Need help choosing a voltage stabilizer

Question

Electronics

Good afternoon!
Need help on the following issues:

1. Current stabilizer. There is an LED (and not one) (3 crystals in each) with a voltage drop of 3-3.4V and a current of 20mA on each crystal (60mA in parallel, 20mA in series, but then the voltage drop is 9-10.2V). The circuit is powered by a Li-ion battery, that is, the voltage varies from 3-4.2V.
In this case, it is not possible to use either a current-limiting resistor (due to the discharge of the battery and as a result of a decrease in current, and hence the brightness of the LEDs), or a circuit based on the LM317, since its power must be at least 6V and without increasing the voltage, which means and efficiency reduction is inevitable.
The last option is to put 2 li-ion batteries in series and start from the LM317, but I would like to reduce the power consumption in the air.
For this task, the price is set first of all, that is, if it turns out to be unreasonably expensive, then I will put 2 batteries in series and LM317 or analogues.
ps device - a portable night light for shooting (I bought a bunch of LEDs - I need to attach it somewhere)

2. 3.3V voltage regulator to power the wireless sensor circuit. Power supply, for example, krone (9V) or other power source with a voltage greater than 3.5V. A low power, high efficiency voltage regulator is required (better than LM2596).
Here, the primary task is to minimize energy consumption, but the price should also be within reason (a couple of dollars for a stabilizer chip (not mass production, I do it for myself, so the retail price))

I hope they will understand me and thank you in advance

Answer 1

1.1 I've seen 20/40 mA precision current regulators somewhere, but I can't remember where. Look.
1.2 It would be possible to use 1 amc7135 and shim it with either a tint or a 555 timer. The latter is slightly cheaper, but not as flexible. After all, sensors can also be hung on a tinka.
2. Why are you not satisfied with the stepdown at 2596? It's cheap, and quite good in terms of efficiency, for such a price. Yes, and a ready-made stepdown costs just over a buck .

Answer 2

1. I think it's called an LED driver. Look through here: www.chipdip.ru/catalog/ic-led-drivers/ ? It looks like there are datasheets.