Apparatus is provided for use with a subject's body, vagina, vaginal fornix, uterus, and uterine artery. A fornix-engaging structure is inserted into the vagina and engages the vaginal fornix. A rod is inserted into the subject's body via the fornix-engaging structure, such that a distal end of the rod passes through vaginal tissue at a first vaginal site until the distal end of the rod is at a first extrauterine site outside of the uterine artery, but in a vicinity of a portion of the uterine artery that supplies a uterine fibroid. A rod-guide is coupled to the fornix-engaging structure, and guides the distal end of the rod to the first extrauterine site. A uterine artery compression device is disposed on the distal end of the rod. Other embodiments are also described.