Space debris at low Earth orbits (LEO) in the size range of 1 to 10 cm in diameter poses a severe threat on the International Space Station and other valuable space assets. High-power laser radiation may be the most feasible means to mitigate this problem. Under the irradiation of a high-power laser beam part of the debris material is ablated and provides an impulse to the debris fragment. Proper direction of the impulse vector allows either to deflect the object trajectory to miss the station (defense option) or to reduce the orbital energy of the debris and force it on a trajectory through the upper atmosphere. There the debris burns up instantaneously or after a few revolutions (cleaning option for LEO). A space based deployment of the laser is favored for several reasons: The lack of laser transmission through the atmosphere reduces the total the total system substantially, laser range and detection requirements are inferior and the laser can be used against an immediate threat. Peculiarities of the geometrical situation in the orbital plane are described. Based on a 100 kW average power laser, aluminum as a typical material, and some other assumptions, the capability and limitations with respect to the debris velocity and mass are calculated for both options of the laser utilization.