The Defiant-class USS Murgatroid is the only other ship in the fleet (apart from its prototype assigned to Deep Space Nine in the Bajor system) equipped with a Romulan Cloaking Device, and the only ship in the fleet required by direct order of the admiralty to keep its cloak active at all times.
The Murgatroid's crew has been referred to as the Federation's Foreign Legion. Misfits and troublemakers who cannot fit in anywhere else in Starfleet often end up on the Murgatroid. Both discipline and adherence to UFP regulations and mores are rather lax on the Murgatroid; but Starfleet Command doesn't seem to object often as long as the Murgatroid stays out of sight; or at least, out of the way. Starfleet occasionally sends the Murgatroid out on covert missions, when the top brass want deniability but aren't too concerned with results. The Murgatroid seems to wander more-or-less at random, their destinations and reasons known only to themselves. Their shore leaves are legendary.