A crimper for a balloon-expandable prosthetic heart valve, the prosthetic heart valve having a tubular balloon-expandable support frame defining a cylindrical space within which a plurality of flexible leaflets are attached, the leaflets being configured to coapt against one another, the support frame defining an expanded diameter D max in an expanded state, the crimper comprising: a base on which are fixedly mounted first and second disk-shaped walls that define a central axis and are axially spaced apart, and first and second outer rims, the first outer rim extending from the first disk-shaped wall toward and contacting the second outer rim extending from the second disk-shaped wall, each of the first and second disk-shaped walls having twelve evenly spaced spoke-like radially-oriented guiding slits of at least 5 mm in length formed therein; twelve movable jaws arrayed in a nested circle around the central axis, being axially and rotatably constrained by but radially movable positioned between the first and second disk-shaped walls and circumferentially surrounded by the outer rims, each jaw being formed of a single piece, being substantially radially oriented and having an outer head portion, each jaw having axially-projecting camming members extending from opposite sides of the jaw into the guiding slits, each jaw further having a recess forming a narrowed bridge between the head portion and a radially inner wedge-shaped finger that ends in a jaw tip and has a radially inner face, wherein the combination of all the radially inner faces defines a variable-sized crimping aperture centered about the central axis, and wherein the camming members and jaw tip of each jaw align along a radial line through the central axis and each jaw nests with the recess of an adjacent jaw; a pair of cam plates, each cam plate being rotatable about the central axis relative to and positioned axially outside of the first and second disk-shaped walls, each cam plate including a plurality of spiral cam tracks centered around the central axis configured to receive and act directly on a plurality of the camming members that extend through the guiding slits without any intervening linkage and radially move the jaws along the guiding slits to open or close the variable-sized crimping aperture; a handle connected to simultaneously rotate both of the cam plates; a stop member positioned to stop rotation of the handle and thus limit the minimum size of the crimping aperture; wherein displacing the handle until the handle contacts and is stopped by the stop member rotates the cam plates such that the spiral cam tracks contact the camming members on both sides of each jaw and apply radially inward forces to the jaws sufficient to narrow the crimping aperture to a closed configuration and crimp the heart valve down to a reduced diameter D min that is at least 10 mm less than the expanded diameter D max. a base on which are fixedly mounted first and second disk-shaped walls that define a central axis and are axially spaced apart, and first and second outer rims, the first outer rim extending from the first disk-shaped wall toward and contacting the second outer rim extending from the second disk-shaped wall, each of the first and second disk-shaped walls having twelve evenly spaced spoke-like radially-oriented guiding slits of at least 5 mm in length formed therein; twelve movable jaws arrayed in a nested circle around the central axis, being axially and rotatably constrained by but radially movable positioned between the first and second disk-shaped walls and circumferentially surrounded by the outer rims, each jaw being formed of a single piece, being substantially radially oriented and having an outer head portion, each jaw having axially-projecting camming members extending from opposite sides of the jaw into the guiding slits, each jaw further having a recess forming a narrowed bridge between the head portion and a radially inner wedge-shaped finger that ends in a jaw tip and has a radially inner face, wherein the combination of all the radially inner faces defines a variable-sized crimping aperture centered about the central axis, and wherein the camming members and jaw tip of each jaw align along a radial line through the central axis and each jaw nests with the recess of an adjacent jaw; a pair of cam plates, each cam plate being rotatable about the central axis relative to and positioned axially outside of the first and second disk-shaped walls, each cam plate including a plurality of spiral cam tracks centered around the central axis configured to receive and act directly on a plurality of the camming members that extend through the guiding slits without any intervening linkage and radially move the jaws along the guiding slits to open or close the variable-sized crimping aperture; a handle connected to simultaneously rotate both of the cam plates; a stop member positioned to stop rotation of the handle and thus limit the minimum size of the crimping aperture; wherein displacing the handle until the handle contacts and is stopped by the stop member rotates the cam plates such that the spiral cam tracks contact the camming members on both sides of each jaw and apply radially inward forces to the jaws sufficient to narrow the crimping aperture to a closed configuration and crimp the heart valve down to a reduced diameter D min that is at least 10 mm less than the expanded diameter D max.