In a self-propelled construction machine (1), in particular road milling machine or surface miner, for working a ground pavement, comprising a milling drum (10), which is mounted in a machine frame, wherein a milling cut develops during milling of the ground pavement with the milling drum (10), wherein the milling drum (10) comprises a first and a second end side, at least a first measuring device, which is arranged next to the first end side of the milling drum (10) and measures the distance of the machine frame relative to the ground pavement next to the first end side of the milling drum (10), at least a second measuring device, which is arranged next to the second end side of the milling drum (10) and measures the distance of the machine frame relative to the ground pavement next to the second end side of the milling drum (10), and a control device (40) for controlling the milling depth, wherein, in a first milling operation, the control device (40) determines the milling depth by means of measurements performed by the first and the second measuring device, it is provided for the following features to be achieved: a second milling operation is detectable by means of the control device (40), in which the milling drum (10) is positioned on an as yet non-milled milling cut that is arranged next to a previously milled milling cut, wherein the control device (40), as soon as the second milling operation is detected, uses measurements performed by at least a third measuring device in lieu of the first and/or the second measuring device for determining the milling depth.