Laminar-turbulent breakdown in a swept-wing boundary layer is typically caused by secondary instabilities of steady crossflow vortices (CFVs). So far, boundary-layer suction for laminar flow control in three-dimensional boundary layers has been applied to reduce the crossflow and thus the growth of the primary vortices only. We investigate the influence of strong, localized suction (pinpoint suction) on high-amplitude CFVs and their secondary instability. The highly concentrated suction necessary enforces however a high wall-normal resolution near the wall and careful grid studies to get converged results with our incompressible code based on the vorticity-velocity formulation of the equations. We show the successful application of pinpoint suction resulting in a significant delay of laminar-turbulent transition. The incompressible results are verified with our compressible code at Ma=0.2 using modeled suction holes. For Ma=0.8 we compare a modeled-suction result with a simulation that includes the interaction of the boundary-layer flow with the suction-channel flow.