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The multimodal method is used to develop an approach for optimizing the shape of axisymmetric acoustic horns for both well-controlled directivity and high radiation efficiency over a wide frequency range. A horn with an arbitrary profile can be efficiently modeled with the multimodal method by projecting the wave field over transverse modes in connected short cylinders; the radii of the cylinders are used directly as design variables. Many design variables are employed in the optimization process to ensure design flexibility and computational accuracy. The relative weights for the design objectives of constant directivity, high radiation efficiency, and acceptable shape smoothness are adjusted by two coefficients in the objective function. The optimization problem is solved with a gradient-based algorithm, which takes advantage of algebraic gradient expressions. Numerical experiments demonstrate that the optimization procedure generates smooth horn contours that exhibit considerably improved performance over the target frequency band. Interestingly, a high-quality horn produced with moderate weight coefficients is similar in shape to constant-directivity horns invented earlier while having good low-frequency loading properties. The proposed method provides an attractive alternative to conventional horn design approaches.