One thing I really liked in a previous job was a split daytime-vs-nighttime rotation. It was well worth a little annoyance to set up in our tools. One week you'd be the 'daytime' oncall for business hours (something like 9-5 Mon-Fri, though we might have tweaked those hours a bit; it might have been 10-6 or something). The next you'd be on call for the complementary time (5-9, weekends). You were on call for the same total amount of time, just smeared over two different weeks. It ended up being less of a burden to optimize your schedule for a reasonable response time, but operational work still got done. And in practice awareness of operational issues was not too hard to maintain between the two members of the split.
(I think the best thing, if you can swing it, is probably a follow-the-sun rotation where there are three teams distributed 8 hours apart around the globe, and they trade off 8-hour workday shifts. But a lot of uncommon things probably have to be true of your organization for that idea to even be on the radar.)