A laser beam directed is moved relative to a workpiece to weld along a weld seam and form a weld pool in the area surrounding the laser beam. The weld pool has a characteristic oscillation frequency fco, and a laser power is modulated with a modulation frequency f and a modulation amplitude Π=1−Pmin/Pmax, where Pmin is minimal and Pmax is maximal laser power during a modulation period. For a normalized characteristic oscillation frequency Λco and a normalized modulation frequency Λ, Λ≥2.2*Λco, with Λ=f·df/ν, where ν is the feed rate of the laser beam, and df is diameter of a beam focal spot. Also, Λco=f,cotest·df,cotest/vcotest, where fcotest is a measured characteristic oscillation frequency, df,cotest the diameter of the beam focal spot, and vcotest is the feed rate of laser beam, all during a test measurement without modulation of the laser power.