A catheter having shaft segments which are joined together by a strong bond providing a low profile shaft section with a flexibility transition and/or a compositional transition. A balloon catheter embodying features of the invention has a distal tip member and a coupling band member surrounding a junction of an inner tubular member of the shaft, and has a gradual change in bending stiffness along a distal end section of the shaft which extends distally from a location within the balloon interior. Another catheter embodying features of the invention has shaft segments joined together by a diagonal seam.