In a method for operating a direct-injection auto-ignition internal combustion engine and a correspondingly configured internal combustion engine including a piston top having integrally formed therein a piston recess which merges into an essentially annular stepped space and an injector forming injection jets directed toward the stepped space, the jets are deflected there in such a way that a first part quantity of fuel is directed in an axial direction and a radial direction into the piston recess, a second part quantity of fuel is deflected in the axial direction and the radial direction over the piston top and third part quantities of fuel are deflected into a circumferential direction so as to impinge one onto the other in the circumferential direction and to be deflected radially inwardly, the start of injection and the injection duration being coordinated with one another and with the crank angle of the internal combustion engine in such a way that the third part quantities of adjacent injection jets meet each other in the circumferential direction with a velocity of at least 15 m/s.