The emission of high-power broad-area semiconductor lasers inherently contains many lateral modes that increase the beam divergence and reduce the spatial coherence. Elimination of higher-order lateral modes from the output beams of commercially available broad-area lasers will be beneficial in many applications of these lasers. Experimental results obtained with a broad-area laser coupled to an anamorphic external cavity are presented and are compared with the predictions from our numerical model. We have predicted and observed with the anamorphic external cavity a greatly improved discrimination against high-order lateral modes. The measurement of the spectrally resolved near-field intensity patterns provides much more comprehensive information on their longitudinal- and lateral-mode content than do observations of near-field and far-field beam intensity profiles. With a broad-area laser of 100-mW nominal power, it has been possible to extract 40% of the maximal power in a stable single-lateral and single-longitudinal mode regime.