This sounds like a bug. I'd look for connections being continually opened without old ones being closed. My own personal style is that once I open a connection, I keep it open as long as possible, until I'm done using it, then explicitlyi close it.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
Also, are you questioning the need to close these resources or the ordering?
I question that you should close a ResultSet when you are closing the corresponding Statement anyway. It just seems to make the code so much more complicated (especially if you try to get the exception handling right), without any benefit.
Ilja, Well yes. But if you have a JDBC framework to run queries this code is only written once. And it seems good to have on the off chance that you are using an old driver that doesn't give all the resources back.