Abstract: A method and apparatus for apodization is exemplified in an ultrasound transducer used, for example, in medical applications. The method and apparatus of the present invention provides an ultrasonic transducer with frequency and amplitude apodization, thus improving signal quality and producing improved ultrasonic images. The manufacture of this apparatus is improved by the making of composite cuts into piezoelectric material according to a predetermined pattern which generally varies the concentration of piezoelectric material across the surface of the transducer. Concentration of piezoelectric material can be varied across the surface of the piezoelectric transducer by varying the spacing between the cuts in the piezoelectric material, or by varying the width of the cuts in the piezoelectric material, or a combination of both.