It seems to be impossible to make a cached thread pool with a limit to the number of threads that it can create.
Here is how static Executors.newCachedThreadPool is
The ThreadPoolExecutor has the following several key behaviors, and your problems can be explained by these behaviors.
When tasks are submitted,
In the first example, note that the SynchronousQueue has essentially size of 0. Therefore, the moment you reach the max size (3), the rejection policy kicks in (#4).
In the second example, the queue of choice is a LinkedBlockingQueue which has an unlimited size. Therefore, you get stuck with behavior #2.
You cannot really tinker much with the cached type or the fixed type, as their behavior is almost completely determined.
If you want to have a bounded and dynamic thread pool, you need to use a positive core size and max size combined with a queue of a finite size. For example,
new ThreadPoolExecutor(10, // core size
50, // max size
10*60, // idle timeout
TimeUnit.SECONDS,
new ArrayBlockingQueue(20)); // queue with a size
Addendum: this is a fairly old answer, and it appears that JDK changed its behavior when it comes to core size of 0. Since JDK 1.6, if the core size is 0 and the pool does not have any threads, the ThreadPoolExecutor will add a thread to execute that task. Therefore, the core size of 0 is an exception to the rule above. Thanks Steve for bringing that to my attention.