Embodiments of the present disclosure provide a delivery apparatus for a prosthetic heart valve. Disclosed steerable catheters can include a handle, a steerable shaft extending from the handle, and a pull wire. The shaft can include a main lumen, an inner polymeric layer surrounding the main lumen, a braided layer surrounding the inner polymeric layer, and an outer polymeric layer surrounding the braided layer, the outer polymeric layer defining a pull wire lumen. The pull wire can extend from the handle and through the pull wire lumen and can have a distal end portion coupled to a distal end portion of the shaft.