Prepare for the SCJP test - even if you aren't going to take it.
You mentioned that you don't want a book that's going over things you already know. I highly recommend SCJP for Java 6 Study Guide. I got this book (the Java 5 version) to study for the test, and even though I already knew and was working with Java full time, it did not insult my intelligence even while going over the fundamental basics of the language.
Even though I was already competent, I learned important details about the language throughout the book, including specific details about the access keywords, polymorphism, as well as overloaded method priority, which became a lot more important when generics and auto-boxing were added.
From there, you may actually want to take the test (though at $200-300, whatever it is now, it would be better for an employer to subsidize it for you). The next level test, SCJD (D for Developer), actually requires you to implement a basic program with a back- and front-end, which would be a great way to get a basic, small (20-40 hour), well-defined project to cut your teeth on.