They encourage you do use the American Eagle bus to do an inter-terminal transfer since you stay in a secured environment. If you arrive in T4 and need to head to T3, follow the signs to the American Eagle gate (I think it is 44 but I could be wrong). Take the bus to the AE terminal and switch to the bus heading to T3 (ask the driver - they can tell you).

If you are in T3, DO NOT follow the signs to baggage claim since you will not be secure. There should be signs to Gate 39 (again, I think) for American Eagle connections. Take the bus to AE, transfer and they drop you in T4. The total time -- about 20 minutes.

--Jim