An intravascular steerable catheter, comprising; an elongate flexible shaft having a proximal portions and a steerable distal portion, the steerable distal portion of the shaft comprising: a first section, a second section that is proximal relative to, and less flexible or stiffer than, the first section, and a third section that is proximal relative to, and less flexible or stiffer than, the first section and the second section, wherein a stiffness of the second section varies gradually along its length providing a gradual transition over the length of the second section, achieving a smooth, gradual transition between the stiffnesses of the respective first and third sections, and wherein at least one section other than the second section includes a variable stiffness along at least a portion of its length; wherein the stiffness of at least a portion of the third section varies along its length; the third section characterized in that: a first segment that is proximal relative to and adjacent to the second section; and a second segment that is proximal relative to and adjacent to the first segment, wherein the second segment of the third section is less flexible or stiffer than the first segment of the third section, the first section has a substantially constant or distinct stiffness along its length, and the stiffness of the second segment varies alone its length; wherein a rate at which the stiffness changes in the second section is less than a rate at which the stiffness changes in the second segment of the third section. an elongate flexible shaft having a proximal portions and a steerable distal portion, the steerable distal portion of the shaft comprising: a first section, a second section that is proximal relative to, and less flexible or stiffer than, the first section, and a third section that is proximal relative to, and less flexible or stiffer than, the first section and the second section, wherein a stiffness of the second section varies gradually along its length providing a gradual transition over the length of the second section, achieving a smooth, gradual transition between the stiffnesses of the respective first and third sections, and wherein at least one section other than the second section includes a variable stiffness along at least a portion of its length; wherein the stiffness of at least a portion of the third section varies along its length; the third section characterized in that: a first segment that is proximal relative to and adjacent to the second section; and a second segment that is proximal relative to and adjacent to the first segment, wherein the second segment of the third section is less flexible or stiffer than the first segment of the third section, the first section has a substantially constant or distinct stiffness along its length, and the stiffness of the second segment varies alone its length; wherein a rate at which the stiffness changes in the second section is less than a rate at which the stiffness changes in the second segment of the third section. a first section, a second section that is proximal relative to, and less flexible or stiffer than, the first section, and a third section that is proximal relative to, and less flexible or stiffer than, the first section and the second section, wherein a stiffness of the second section varies gradually along its length providing a gradual transition over the length of the second section, achieving a smooth, gradual transition between the stiffnesses of the respective first and third sections, and wherein at least one section other than the second section includes a variable stiffness along at least a portion of its length; wherein the stiffness of at least a portion of the third section varies along its length; the third section characterized in that: a first segment that is proximal relative to and adjacent to the second section; and a second segment that is proximal relative to and adjacent to the first segment, wherein the second segment of the third section is less flexible or stiffer than the first segment of the third section, the first section has a substantially constant or distinct stiffness along its length, and the stiffness of the second segment varies alone its length; wherein a rate at which the stiffness changes in the second section is less than a rate at which the stiffness changes in the second segment of the third section. a first segment that is proximal relative to and adjacent to the second section; and a second segment that is proximal relative to and adjacent to the first segment, wherein the second segment of the third section is less flexible or stiffer than the first segment of the third section, the first section has a substantially constant or distinct stiffness along its length, and the stiffness of the second segment varies alone its length; wherein a rate at which the stiffness changes in the second section is less than a rate at which the stiffness changes in the second segment of the third section.