peelessly

adv. Done with a bladder as wide open--er, empty--as the great outdoors.

Real citation: "3:21 p.m. A guy with a ponytail and goatee took a whiz behind a Ninth Street building, then peelessly headed for the Plaza."
(Kevin L. Hoover, "Seething weirdosity exudes from Arcata's every orifice," The Arcata Eye, http://www.arcataeye.com/police/051005police.shtml)

Made-up citation: “Male rats deal with few issues peelessly. ‘Walk over it and pee on it’ is pretty much their approach to everything.”