I would NOT recommend the Winchester 240 JSP's for deer in a pistol. One of my shooting buddies shot a doe from 25 yards with his scoped Encore - witnessed the bullet enter it's left lung area, - saw the cloud of dust from the exit wound where the bullet hit the ground - and the deer ran off. The bullet was recovered from the dirt with no signs of expansion whatsoever. They spent the rest of the remaining daylight looking for the deer and saw no signs of it whatsoever.
He's since moved to a 180gr XTP handload with H110. I load 240gr XTP's under 2400 or 5744 at around 1800fps in my Rossi break action. I once heard a second hand quote from a Ruger Rep that the RedHawk can handle absolutely anything you can throw at it - so don't be afraid of stout loads using heavy bullets - just work your way up to them.