I was a FT software engineer and software engineering manager. You can sort of combine techniques to get to a 3 day week and proportional compensation. This is sort of what
@mtnrider said above, with a few tweaks:
1. Start as a full time engineer.
2. Work for a while and build up / save up vacation time.
3. Ask for FMLA / personal leave. At my last company personal leave could be intermittent and taken in 4 hour chunks and you could get up to 12 weeks of personal leave, but it had to be approved by a VP. Most everyone qualifies for FMLA as long as you've been FT for a year. I think California even has "enhanced FMLA" if you're there.
4. Take FMLA leave in one hour chunks every Friday.
5. Start taking your accrued vacation time by taking every Monday off.
6. Voila, three day weeks.
If you're really burned out or are in reorg-ville or between projects, or can work from home, you can even stretch not working very hard during those three day weeks. But
@mtnrider's comments are accurate - if you do this then you'll be viewed as a short-timer and will not get promoted and won't get stock options and risk being put in a layoff pool if that happens to happen around the same time (which can be good or bad, depending).
The only other option I know of, and it's hard to find, is if you can find two engineers who work well together and an accommodating company, you can do a job share where each of the two engineers works 20 hours a week and serve as a sort of conjoined-twin FTE.