A holder for a flexible leaflet prosthetic aortic heart valve that is less bulky than earlier holders and minimizes obstructions to vision and working space around the valve to facilitate implantation thereof. The holder may have a central hub and three outwardly extending legs that connect directly and exclusively to tips of the commissures of the aortic heart valve for better tactile feedback when parachuting and seating the valve in the annulus. The legs are sized so that they do not overlap the commissure tips and therefore afford a better view of the sewing ring adjacent the commissures. The legs may be narrow in the midsection or split into two rails to increase visibility of the valve leaflets. The hub may be vaulted axially upward relative to the outer ends of the legs to further increase visibility of the valve. A more secure engagement between the central hub and a delivery handle is also provided to ensure the holder/handle connection does not become loose during suture placement through the sewing ring and fewer handle revolutions are required to screw in and unscrew the handle from the holder.