An improved holder and storage system for a tissue-type prosthetic mitral heart valve that constricts the commissure posts of the valve and prevents suture looping. A rod axially movable relative to the holder tensions lengths of attachment sutures that extend between the commissure post tips to create a tent and flex the tips inward, thus helping to prevent looping of any of an array of pre-implanted sutures around the leading tips during delivery of the valve. The holder has a safety mechanism that prevents valve delivery before the rod is deployed. One embodiment automatically deploys the rod upon opening a storage jar. One embodiment permits a delivery handle to directly deploy the rod, while another uses a separate worm screw and coupling. A holder clip that attaches to a packaging sleeve may be formed of flexible members meshed together from which the heart valve and holder are easily pulled free to eliminate a step of decoupling the clip from the sleeve.