I don't know if better software can replace stupid management but I've been quite happy with Youtrack. That said you can do some extensive micromanagement with that as well, though it requires some coding to do the truly intricate stuff, which just might be enough to prevent the managers from getting any funny ideas ;-)
it's weird why youtrack doesn't come up more often in these types of discussions. It's pretty good, and interestingly enough they now have a "lite" ui mode to simplify it. It's not perfect though, but I've found it hard to find anything better.
There are literally hundreds of competitors out there. But first you have to describe what you like about it. 10-15 years ago everyone would have used something like Request Tracker (RT). There is Redmine, Pivotal Tracker, Trac, Bugzilla. Those are just a few that I recall using. I've probably used more than that.
