Why don't you take a look at PractiTest?
I am biased because I work for them, but on the other hand the system provides all the things you mentioned above that you are looking for (simple to use, good integration with Jira, supports Agile teams, etc) and some additional features and things that make the life of the average tester easier and overall better.
You can sign up to one of the public demos that run once or twice a week from the site. And after the demo you can choose to work with PractiTest for free for a couple of weeks as part of the 2-week free evaluation license.
As you said, testing and test management should not be complex and over-bloated...
-joel