A sheet feeding unit includes a stack elevator which raises the top of a supported stack of sheets to infeed height. A sensor senses the position of the top sheets of the stack, to ascertain whether these exhibit improper left or right offset. Depending upon the magnitude and size of the sensed offset, the stack elevator is correctively shifted, to minimize offset at the top of the stack. Although the sensor is located to only one side of the stack, not at both sides of the stack, it is capable of sensing offset in both left and right directions. When the elevator is lowered, for the laying in of a fresh stack, it is automatically brought to a centered position.