My Thinkpad only supports s2idle (checked the bios no way to turn on s3). It truly sucks, the laptop won't go 8 hours on idle without the battery dying. I used the amd-s2idle tester and it said the laptop was going to idle after 10 minutes but that was not reflected in real world use. Even after turning off every wakeup except the power button to prevent premature wakeup from wifi USB etc.
My only solution was to re-enabling hibernate. It's slower and takes disk space but it works. Laptop can go days on hibernate with no issue.