A system and a method are used for deploying balloon-expandable (i.e., plastically-expandable) prosthetic heart valves (20) so that they assumed their desired operational shape. The system includes a balloon (40) that accommodates non-uniform expansion resistance in the heart valve to expanded to its desired tubular or other shape. The heart valve may have substantially more structural elements adjacent one end, typically the inflow end (22), and the balloon is tapered so as to expand the inflow end before the outflow so that the valve ends up in a tubular shape. Alternatively, a stepped balloon with a larger diameter proximal section adjacent the inflow end of the valve may be used. A method includes applying a non-linear expansion forced to the interior of a plastically- expandable prosthetic heart valve to overcome areas of greater resistance to expansion and result in uniform expansion.