Single crystal semiconductor ingots are pulled from a melt contained in a crucible by a method of controlling the pulling the single crystal in a phase in which an initial cone of the single crystal is grown until a phase in which the pulling of a cylindrical section of the single crystal is begun, by measuring the diameter Dcr of the initial cone of the single crystal and calculating the change in the diameter dDcr/dt; pulling the initial cone of the single crystal from the melt at a pulling rate vp(t) from a point in time t1 until a point in time t2, starting from which the pulling of the cylindrical section of the single crystal in conjunction with a target diameter Dcrs is begun, wherein the profile of the pulling rate vp(t) from the point in time t1 until the point in time t2 during the pulling of the initial cone is predetermined by means of an iterative computation process.