A catheter has a shaft that defines a delivery lumen, for example, to deliver an elongate medical device therethrough; a proximal section of the catheter includes a seal zone portion, a handle portion and a proximal port portion. A relatively thin wall section of the proximal port portion extends between the seal zone portion and a proximal edge that defines part of a perimeter of a proximal opening of the delivery lumen. The handle portion projects laterally from the seal zone portion, generally opposite the relatively thin wall section. An inflation subassembly of the catheter includes a compliant sleeve member and an inflation lumen extending from the sleeve member, proximally along the shaft, and into a connector port formed in the handle portion. The inflation lumen may be formed by fusing a section of a tube to the shaft and molding the handle portion around another section of the tube.