I think what happened is that I realized that the not urgent but important stuff becomes urgent at some point, and then it really has to be done. And it's stressful.
So of late, I'm much better about doing things that are important before they become urgent, and that helps a lot with my stress.
There's not much in my work life that's in the not important/not urgent category. Honestly, by the time it gets to my desk, someone things it's important, even if not immediately urgent.
A few things get to my desk that feel urgent but unimportant to me, but I know they're important to someone, and so they are important. And I do get things that are important and urgent right off, but that's usually because they're emerging problems, and the urgency and importance are real.
This long weekend, for example: I've read a thesis prospectus and given feedback; graded two stacks of assignments and given feedback; done a small house project; done laundry; cleaned the house a bit; read a play. None of those things absolutely had to be done by Monday. And I do have several things on my list still. But my stress about Monday and next week has gone down a lot since I finished the stuff that would have become urgent some time next week.
I have stuff that will become urgent by the 15th of December. Four things in one category, two in another. But those aren't urgent yet, so I can try to get one done tomorrow, and then there will be fewer to do.
I'll admit, I felt a bit stressed out on Wednesday night, but I've plugged away at things without urgency, and gotten them done, and now I feel less stressed about Monday.
Another thing I've really taken to heart is that I'm everyone's chair. Even if I'm cranky at someone, if they ask me for help with something, I do my best to help them. I think I've risen well to that, though I would have had my doubts before I became chair. That doesn't mean that everything works out and everyone gets everything they want, but I do my part.
I do admit that I wish that some of the on campus folks would decide if they REALLY need a full letter of recommendation from the chair for this or that. I think they really don't, much of the time. And it usually takes me about two hours to write a fairly short letter of recommendation (a page and a half, say). But I don't want colleagues to miss out on something because I didn't make a real effort and some other chair did.
I'm more eager than ever for retirement. I suppose that's a good thing to learn. And the holiday, which we started on Wednesday, has been really helpful in letting me have plenty of relaxation time with some time to do stuff that was important if not urgent.