Here's something for Black Pudding 7. I haven't used this in play, but of course I played around with it myself and kinda dig it. Maybe it's not new, I'm not sure. I hadn't seen it.
This method does not get you a nice bell curve. For example, it's far easier to get an 18 since it is a 1 in 8 chance. If I was "gaming the system" with this, I'd just always roll that d8. Which, of course, is totally valid. It's your choice. You aren't breaking anything
Just rolling the d4 all the way gives you an average PC that has no negative and three +1 stats... which is pretty nice too.
EDIT: I posted this in haste from an old thing I forgot about and it has shitty formatting so you should ignore it. I didn't proofread bc nobody got time for that.