The present invention provides a prosthetic heart valve device with improved fit and/or apposition between the device frame and left atrial tissue and/or the device base and the annular tissue of the left atrium to improve shifting of the implanted device and/or mitigate paravalvular leakage. The improved fit and/or apposition arises in various embodiments by providing or allowing an asymmetrical frame and/or frame base and/or providing a lower lip to aid in conforming to the asymmetrical shape of the atrium and/or ensure firm positioning therein. An additional benefit of these arrangement(s) is mitigation of paravalvular leakage as a result of improved fit and seal. In certain embodiments, the asymmetry of the frame assists with delivery of the device into the atrium.