A balloon for a balloon catheter comprising: a proximal cone section having proximal and distal ends (136b, 136a), a length extending between the proximal and distal ends, and an exterior surface; a distal cone section having proximal and distal ends (136a, 136b), a length extending between the proximal and distal ends, and an exterior surface; and a balloon body section extending between and interconnecting the distal end of the proximal cone section and the proximal end of the distal cone section, the proximal and distal cone sections (128b, 128a) and the balloon body section defining an interior chamber configured to receive fluid to expand the balloon from a non-expanded state to an expanded state in which the proximal cone section has a generally conical shape and a circumference tapering proximally toward the proximal end of the proximal cone section, and the distal cone section has a generally conical shape and a circumference tapering distally toward the distal end of the distal cone section, wherein at least one of the proximal and distal cone sections (128b, 128a) includes a plurality of grooves defined by alternating inner and outer fold lines (149b, 149a) spaced around the circumference of said at least one of the proximal and distal cone sections (128b, 128a), the grooves each having a length extending generally lengthwise of said at least one of the proximal and distal cone sections (128b, 128a), a depth extending inward from the exterior surface of said at least one of the proximal and distal cone sections (128b, 128a) to a bottom of the groove, and a width extending circumferentially of said at least one of the proximal and distal cone sections (128b, 128a), wherein each groove has a distal end section, a proximal end section, and a central section between the distal and proximal end sections (160a, 160b), wherein the depth of each groove tapers proximally at its proximal end section toward the proximal end of the groove, wherein the depth of each groove tapers distally at its distal end section toward the distal end of the groove, wherein minimum depths of each groove are located generally at the proximal and distal end sections (160b, 160a) of the groove, and wherein the depth of each groove at its central section is its maximum depth. a proximal cone section having proximal and distal ends (136b, 136a), a length extending between the proximal and distal ends, and an exterior surface; a distal cone section having proximal and distal ends (136a, 136b), a length extending between the proximal and distal ends, and an exterior surface; and a balloon body section extending between and interconnecting the distal end of the proximal cone section and the proximal end of the distal cone section, the proximal and distal cone sections (128b, 128a) and the balloon body section defining an interior chamber configured to receive fluid to expand the balloon from a non-expanded state to an expanded state in which the proximal cone section has a generally conical shape and a circumference tapering proximally toward the proximal end of the proximal cone section, and the distal cone section has a generally conical shape and a circumference tapering distally toward the distal end of the distal cone section, wherein at least one of the proximal and distal cone sections (128b, 128a) includes a plurality of grooves defined by alternating inner and outer fold lines (149b, 149a) spaced around the circumference of said at least one of the proximal and distal cone sections (128b, 128a), the grooves each having a length extending generally lengthwise of said at least one of the proximal and distal cone sections (128b, 128a), a depth extending inward from the exterior surface of said at least one of the proximal and distal cone sections (128b, 128a) to a bottom of the groove, and a width extending circumferentially of said at least one of the proximal and distal cone sections (128b, 128a), wherein each groove has a distal end section, a proximal end section, and a central section between the distal and proximal end sections (160a, 160b), wherein the depth of each groove tapers proximally at its proximal end section toward the proximal end of the groove, wherein the depth of each groove tapers distally at its distal end section toward the distal end of the groove, wherein minimum depths of each groove are located generally at the proximal and distal end sections (160b, 160a) of the groove, and wherein the depth of each groove at its central section is its maximum depth.