A prosthetic valve includes a tubular valve body, snares, and an upstream support. A native valve of a heart of a subject is disposed between an atrium and a ventricle of the heart, and has an annulus and leaflets. The prosthetic valve is advanced to the heart while in a compressed state. The prosthetic valve is positioned within the heart such that the snares are disposed upstream of the annulus and leaflets. The snares are expanded radially outwardly upstream of the leaflets. Subsequently, the prosthetic valve is moved in a downstream direction such that the snares become disposed downstream of the leaflets. While the snares remain downstream of the leaflets, the upstream support is expanded within the atrium, and the upstream support is placed against an upstream surface of the annulus. Other embodiments are also described.
