Self-propelled construction machine, in particular road milling machine or surface miner, for working a ground pavement, comprising - a milling drum, which is mounted in a machine frame, wherein a milling cut develops during milling of the ground pavement with the milling drum, wherein the milling drum comprises a first and a second end side (11, 13), - at least one first measuring device, which is arranged next to the first end side of the milling drum and measures the distance of the machine frame relative to the ground pavement next to the first end side of the milling drum, - at least one second measuring device, which is arranged next to the second end side of the milling drum and measures the distance of the machine frame relative to the ground pavement next to the second end side of the milling drum, - at least one third measuring device, and - a control device for controlling the milling depth, wherein, in a first milling operation, the control device determines the milling depth by means of measurements performed by the first and the second measuring device (30, 32), characterized in that the control device is configured such that a second milling operation is detectable by means of the control device, in which the milling drum is positioned on an as yet non-milled milling cut that is arranged next to a previously milled milling cut, wherein the control device is configured such that, as soon as the second milling operation is detected, it uses measurements performed by the at least one third measuring device in lieu of the first or the second measuring device (30, 32) for determining the milling depth, wherein the control device is configured to verify whether the construction machine, after the second milling operation, mills in the first milling operation once again, and the control device is configured to determine, as soon as renewed milling in the first milling operation is ascertained, the milling depth once again by means of measurements performed by the first and the second measuring device (30, 32), wherein the control device is configured to verify, for ascertaining renewed milling in the first milling operation, the time and/or the distance travelled by the construction machine and to compare the same with a specified time and/or travel distance. - a milling drum, which is mounted in a machine frame, wherein a milling cut develops during milling of the ground pavement with the milling drum, wherein the milling drum comprises a first and a second end side (11, 13), - at least one first measuring device, which is arranged next to the first end side of the milling drum and measures the distance of the machine frame relative to the ground pavement next to the first end side of the milling drum, - at least one second measuring device, which is arranged next to the second end side of the milling drum and measures the distance of the machine frame relative to the ground pavement next to the second end side of the milling drum, - at least one third measuring device, and - a control device for controlling the milling depth, wherein, in a first milling operation, the control device determines the milling depth by means of measurements performed by the first and the second measuring device (30, 32), the control device is configured such that a second milling operation is detectable by means of the control device, in which the milling drum is positioned on an as yet non-milled milling cut that is arranged next to a previously milled milling cut, wherein the control device is configured such that, as soon as the second milling operation is detected, it uses measurements performed by the at least one third measuring device in lieu of the first or the second measuring device (30, 32) for determining the milling depth, wherein the control device is configured to verify whether the construction machine, after the second milling operation, mills in the first milling operation once again, and the control device is configured to determine, as soon as renewed milling in the first milling operation is ascertained, the milling depth once again by means of measurements performed by the first and the second measuring device (30, 32), wherein the control device is configured to verify, for ascertaining renewed milling in the first milling operation, the time and/or the distance travelled by the construction machine and to compare the same with a specified time and/or travel distance.