A true-to-life Wizard of The Old Times, an ashipu was the Mesopotamian equivalent of a shaman or witch doctor. A member of the Babylonian priesthood, their primary task was to diagnose any ailments, which always came in the forms of various demons. For example, there was a toothache demon, a skin lesion demon, a fever demon, and so on.
Some of their tactics have trickled down throughout the ages to today. They crafted voodoo dolls out of wax to represent the demons, which they proceeded to melt down, presumably killing the demon; they would sprinkle water as a purifying agent, and they would place plants outside rooms to ward off evil spirits. Needless to say, they are often referred to in text as "exorcists" rather than doctors or even merely priests.
In general, the ashipus avoided any actual medical practices, usually relegating that to the asu, who helped promote the ideas of basic hygiene, bandages, and sterilization as tenets of good medicine. This lack of pragmatism combined with their spiritual agenda makes them some of history's earliest fundamentalists.
Ashipus more or less predate Hammurabi in the region, and were fairly quickly overtaken by the asu and actual doctors who began using the more time-honored witchcraft of pills and surgery to fix their patients.