Method for machining a workpiece using a machining system, the machining system comprising a tool which can be rotated about a tool axis and has a first machining zone for a first type of machining, wherein the first machining zone is oriented on the tool such that, when a workpiece is being machined by way of the first machining zone, a first process force which is related to the first type of machining and acts on the tool has a first component, which acts parallel to the tool axis in a main direction, wherein the tool is designed in the form of a double tool, which also has a second machining zone for a second type of machining, wherein the second machining zone is oriented on the tool such that, when a workpiece is being machined by way of the second machining zone, a second process force which is related to the second type of machining and acts on the tool has a second component, which acts parallel to the tool axis counter to the main direction, wherein the machining system also comprises a spring retainer, wherein the spring retainer has a main body and a holding body, wherein the tool is fastened directly or indirectly on the holding body of the spring retainer, wherein the main body and the holding body are displaceable in relation to one another along the tool axis, wherein a main stop is provided on the main body and delimits displacement of the holding body towards the main body in the main direction, and wherein the holding body is prestressed against the main stop by a spring element of the spring retainer and can be lifted off from the main stop, in a direction counter to the main direction, counter to the spring force of the spring element, characterized in that, in a first step, the workpiece is machined by way of the first machining zone, wherein the first component of the first process force related to the first type of machining presses the holding body, in addition to the spring force, against the main stop of the main body, and in that, in a second step, the workpiece is machined by way of the second machining zone, wherein the holding body is lifted off from the main stop of the main body, so that the tool is pressed against the workpiece by the spring force of the spring element. the machining system comprising a tool which can be rotated about a tool axis and has a first machining zone for a first type of machining, wherein the first machining zone is oriented on the tool such that, when a workpiece is being machined by way of the first machining zone, a first process force which is related to the first type of machining and acts on the tool has a first component, which acts parallel to the tool axis in a main direction, wherein the tool is designed in the form of a double tool, which also has a second machining zone for a second type of machining, wherein the second machining zone is oriented on the tool such that, when a workpiece is being machined by way of the second machining zone, a second process force which is related to the second type of machining and acts on the tool has a second component, which acts parallel to the tool axis counter to the main direction, wherein the machining system also comprises a spring retainer, wherein the spring retainer has a main body and a holding body, wherein the tool is fastened directly or indirectly on the holding body of the spring retainer, wherein the main body and the holding body are displaceable in relation to one another along the tool axis, wherein a main stop is provided on the main body and delimits displacement of the holding body towards the main body in the main direction, and wherein the holding body is prestressed against the main stop by a spring element of the spring retainer and can be lifted off from the main stop, in a direction counter to the main direction, counter to the spring force of the spring element, characterized in that, in a first step, the workpiece is machined by way of the first machining zone, wherein the first component of the first process force related to the first type of machining presses the holding body, in addition to the spring force, against the main stop of the main body, and in that, in a second step, the workpiece is machined by way of the second machining zone, wherein the holding body is lifted off from the main stop of the main body, so that the tool is pressed against the workpiece by the spring force of the spring element.