A method of implanting a prosthetic heart valve within a patient can comprise inserting a distal end portion of a delivery apparatus and a prosthetic heart valve into the patient and advancing the prosthetic heart valve to a deployment location within the heart of the patient and inflating one or more of a plurality of differently-sized balloons in a balloon-assembly on the distal end portion of the delivery apparatus. The prosthetic heart valve can be mounted on the balloon assembly in a crimped state and the inflating of the one or more of the plurality of differently-sized balloons can expand the prosthetic heart valve from the crimped state to a radially expanded state having a non-cylindrical shape.