A delivery system for delivering a prosthetic heart valve to a native valve site within the human vasculature. The prosthetic valve is disposed on a balloon at the end of a balloon catheter. The balloon catheter passes through a delivery sleeve assembly and handle. A pull wire travels from the handle to a distal end of the delivery sleeve assembly. Actuation of the handle pulls on the pull wire, which causes openings in a slotted tube of the delivery sleeve assembly to close, thus causing the delivery sleeve assembly to bend. A stretchable cover is placed over the slotted tube for biasing the steerable catheter toward a straight position. Once advanced to the native valve site, the prosthetic valve is deployed by inflating the balloon.