A multi-stage delivery system (100; 100') for controlled deployment of a replacement heart valve by limiting the amount of expansion during the various stages, the multi-stage delivery system (100; 100') comprising: an elongate inner member comprising a proximal end and a distal end; an inner retention ring (112; 112') on the elongate inner member, the ring (112; 112') being configured to engage a radially compacted proximal end of a frame of the replacement heart valve; a support tube (108; 108') configured to be slidable over the elongate inner member and the inner retention ring (112; 112') and configured to cover at least the radially compacted proximal end of the frame of the replacement heart valve when the proximal end of the frame of the replacement heart valve is engaged with the inner retention ring (112; 112'); and an outer sheath (110; 110') configured to be slidable over the support tube (108; 108') and configured to cover a distal end of the frame of the replacement heart valve to retain the frame of the replacement heart valve in a radially compacted configuration when the proximal end of the frame of the replacement heart valve is covered by the support tube (108; 108') and engaged with the inner retention ring (112; 112'); wherein the delivery system (100; 100') is configured such that when the proximal end of the frame of the replacement heart valve is both engaged with the inner retention ring (112; 112') and covered by the support tube (108; 108'), and when the distal end of the frame of the replacement heart valve is covered by the outer sheath (110; 110'): proximal retraction of the outer sheath (110; 110') relative to the elongate inner member exposes the distal end of the frame of the replacement heart valve and allows the distal end of the frame of the replacement heart valve to radially expand while the proximal end of the frame of the replacement heart valve remains covered by the support tube (108; 108'); and proximal retraction of the support tube (108; 108') relative to the elongate inner member exposes the proximal end of the frame of the replacement heart valve and allows the proximal end of the frame of the replacement heart valve to radially expand; and wherein movement of the support tube (108; 108') is independent of movement of the outer sheath (110; 110'). an elongate inner member comprising a proximal end and a distal end; an inner retention ring (112; 112') on the elongate inner member, the ring (112; 112') being configured to engage a radially compacted proximal end of a frame of the replacement heart valve; a support tube (108; 108') configured to be slidable over the elongate inner member and the inner retention ring (112; 112') and configured to cover at least the radially compacted proximal end of the frame of the replacement heart valve when the proximal end of the frame of the replacement heart valve is engaged with the inner retention ring (112; 112'); and an outer sheath (110; 110') configured to be slidable over the support tube (108; 108') and configured to cover a distal end of the frame of the replacement heart valve to retain the frame of the replacement heart valve in a radially compacted configuration when the proximal end of the frame of the replacement heart valve is covered by the support tube (108; 108') and engaged with the inner retention ring (112; 112'); wherein the delivery system (100; 100') is configured such that when the proximal end of the frame of the replacement heart valve is both engaged with the inner retention ring (112; 112') and covered by the support tube (108; 108'), and when the distal end of the frame of the replacement heart valve is covered by the outer sheath (110; 110'): proximal retraction of the outer sheath (110; 110') relative to the elongate inner member exposes the distal end of the frame of the replacement heart valve and allows the distal end of the frame of the replacement heart valve to radially expand while the proximal end of the frame of the replacement heart valve remains covered by the support tube (108; 108'); and proximal retraction of the support tube (108; 108') relative to the elongate inner member exposes the proximal end of the frame of the replacement heart valve and allows the proximal end of the frame of the replacement heart valve to radially expand; and proximal retraction of the outer sheath (110; 110') relative to the elongate inner member exposes the distal end of the frame of the replacement heart valve and allows the distal end of the frame of the replacement heart valve to radially expand while the proximal end of the frame of the replacement heart valve remains covered by the support tube (108; 108'); and proximal retraction of the support tube (108; 108') relative to the elongate inner member exposes the proximal end of the frame of the replacement heart valve and allows the proximal end of the frame of the replacement heart valve to radially expand; and wherein movement of the support tube (108; 108') is independent of movement of the outer sheath (110; 110').