A prosthetic heart valve for replacement of a native heart valve having a native valve annulus, comprising: (a) a stent body having a proximal end and a distal end and including a generally tubular annulus region and a flare section proximal to the annulus region, the stent body having a proximal-to-distal axis, a radially collapsed condition and an unconstrained, fully radially expanded condition, the annulus region and the flare section increasing in diameter during transition from the radially collapsed condition to the radially expanded condition, the annulus region having a substantially constant diameter and the flare section having a greater diameter than the annulus region when the stent body is in the radially expanded condition; (b) one or more prosthetic valve elements mounted to the stent body and operative to allow flow in the antegrade direction through the annulus region but to substantially block flow in the retrograde direction through the annulus region; and (c) a cuff (85; 285) secured to the stent body, the cuff comprising (i) a first cuff portion covering an exterior surface of the annulus region for disposition at the native valve annulus, the first cuff portion having a first diameter when the stent body is in the radially expanded condition, and (ii) a second cuff portion proximal to the first cuff portion, the second cuff portion extending along an exterior surface of the flare section of the stent body, the second cuff portion having a second diameter when the stent body is in the radially expanded condition, the second diameter being greater than the first diameter, the second cuff portion being adapted for engagement with native tissue proximal to the native valve annulus to form a seal with the native tissue which helps to block retrograde flow around the outside of the stent body, the first and second cuff portions being formed from a unitary sheet of material. (a) a stent body having a proximal end and a distal end and including a generally tubular annulus region and a flare section proximal to the annulus region, the stent body having a proximal-to-distal axis, a radially collapsed condition and an unconstrained, fully radially expanded condition, the annulus region and the flare section increasing in diameter during transition from the radially collapsed condition to the radially expanded condition, the annulus region having a substantially constant diameter and the flare section having a greater diameter than the annulus region when the stent body is in the radially expanded condition; (b) one or more prosthetic valve elements mounted to the stent body and operative to allow flow in the antegrade direction through the annulus region but to substantially block flow in the retrograde direction through the annulus region; and (c) a cuff (85; 285) secured to the stent body, the cuff comprising (i) a first cuff portion covering an exterior surface of the annulus region for disposition at the native valve annulus, the first cuff portion having a first diameter when the stent body is in the radially expanded condition, and (ii) a second cuff portion proximal to the first cuff portion, the second cuff portion extending along an exterior surface of the flare section of the stent body, the second cuff portion having a second diameter when the stent body is in the radially expanded condition, the second diameter being greater than the first diameter, the second cuff portion being adapted for engagement with native tissue proximal to the native valve annulus to form a seal with the native tissue which helps to block retrograde flow around the outside of the stent body, the first and second cuff portions being formed from a unitary sheet of material. (i) a first cuff portion covering an exterior surface of the annulus region for disposition at the native valve annulus, the first cuff portion having a first diameter when the stent body is in the radially expanded condition, and (ii) a second cuff portion proximal to the first cuff portion, the second cuff portion extending along an exterior surface of the flare section of the stent body, the second cuff portion having a second diameter when the stent body is in the radially expanded condition, the second diameter being greater than the first diameter, the second cuff portion being adapted for engagement with native tissue proximal to the native valve annulus to form a seal with the native tissue which helps to block retrograde flow around the outside of the stent body, the first and second cuff portions being formed from a unitary sheet of material.