Simple DC step down solution

I'm adapting an existing ps to supply +/- 15-20 vdc to preamp boards that draw zbout 55ma per rail. I'm planning to use an existing transformer and have a simple PSU board to adapt with spare parts to provide the vdc to the boards I've built. Once the AC from the transformer (23-0-23vac) has been converted to VDC via a bridge rectifier it then has some bulk caps. The output voltage is, however, 31.8vdc (unloaded) and I'm looking for a simple way of reducing this to 15-20vdc bearing in mind the 55ma draw of each board. What would you good folk recommend to achieve this? I have a simple option on the existing board to insert a through hole component... The boards have regulators so I just need stable raw power supply that can handle the current draw without smoking...
 
Just use an LM317T regulator. They will handle up to 37V input and you only need two external resistors and a couple of decoupling capacitors. At 55mA you will only generate about 1W of heat so you may need a small heatsink, but nothing significant.
I think I have some of those regulators in the spares box. Are they +/- specific? What size resistor would I need to achieve 20vdc?
 
There's a datasheet here: https://uk.farnell.com/stmicroelectronics/lm317t/v-reg-adj-1-2-37v-to-220-3-317/dp/9756027
See page 9 for the simplest version, but to give better noise performance, I'd stick a 10uF cap on the input, and output at the very least.
Output voltage can be calculated (approximately) using VO = VREF (1 + R2/R1) where VREF=1.25V
For 20V output, I would use R1 = 240 and R2 = 3k6
Make sure it's an LM317T in a TO220 package not one of the tiny surface mount ones!
For the negative voltage, you'll need to use an LM337T regulator. Beware, it's a different pinout!
https://uk.farnell.com/onsemi/lm337t/linear-volt-reg-adj-1-25v-to-220/dp/2564785
Manufacturer types are usually interchangeable.