A prosthetic valve assembly and method of implanting same is disclosed. The prosthetic valve assembly includes a prosthetic valve formed by support frame and valve leaflets, with one or more tethers each having a first end secured to the support frame and the second end attached to, or configured for attachment to, to papillary muscles or other ventricular tissue. The tether is configured and positioned so as to avoid contact or other interference with movement of the valve leaflets, while at the same time providing a tethering action between the support frame and the ventricular tissue. The valve leaflets may be flexible (e.g., so-called tissue or synthetic leaflets) or mechanical.