A fitting for a sealing, non-releasable pipe connection, including a main fitting body for accommodating at least one pipe which is to be connected, and at least one pressing sleeve. The main fitting body and the pressing sleeve have pressing surfaces, which are assigned to one another. The main fitting body has a pressing surface which, in the installed state, is directed towards the pipe which is to be connected, and is assigned to a peripheral region of the main fitting body. The pressing surfaces assigned to one another on the main fitting body and on the pressing sleeve are formed such that the action of pushing the pressing sleeve axially onto the main fitting body gives rise to the peripheral region of the main fitting body being narrowed radially.