ThreadPoolExecutor policy

I'm trying to use a ThreadPoolExecutor to schedule tasks, but running into some problems with its policies. Here's its stated behavior:

1. If fewer than corePoolSize threads are running, the Executor always prefers adding a new thread rather than queuing.
2. If corePoolSize or more threads are running, the Executor always prefers queuing a request rather than adding a new thread.
3. If a request cannot be queued, a new thread is created unless this would exceed maximumPoolSize, in which case, the task will be rejected.

The behavior I want is this:

1. same as above
2. If more than corePoolSize but less than maximumPoolSize threads are running, prefers adding a new thread over queuing, and using an idle thread over adding a new thread.
3. same as above

Basically I don't want any tasks to be rejected; I want them to be queued in an unbounded queue. But I do want to have up to maximumPoolSize threads. If I use an unbounded queue, it never generates threads after it hits coreSize. If I use a bounded queue, it rejects tasks. Is there any way around this?

What I'm thinking about now is running the ThreadPoolExecutor on a SynchronousQueue, but not feeding tasks directly to it - instead feeding them to a separate unbounded LinkedBlockingQueue. Then another thread feeds from the LinkedBlockingQueue into the Executor, and if one gets rejected, it simply tries again until it is not rejected. This seems like a pain and a bit of a hack, though - is there a cleaner way to do this?