In an earlier paper [H. S. C. Wang, J. Acoust. Soc. Am.57, 1076 (1975)], it was demonstrated that amplitude shading of a transducer array can be derived from the minimum property of the total received power except that through a slice of main beam. We show here that in the special and fundamentally important case of linear arrays, the formulation can be simplified by considering the power or object function (OF) to be minimized as a function of a generalized variableu = cosθ − cosθ0, where θ denotes the colatitude angle and θ0the steered direction. Although the total visible range of a linear array covers −2⩽u⩽2, the OF needs only to be minimized in 0⩽u⩽2 due to symmetry of the directivity function. Furthermore, the space 0⩽u⩽2 can be sub‐divided into various regions of different weights to form multiparameter OF for the control of individual sidelobes. As an illustrative example, an endfire array of 12 elements logarithmically spaced over an aperture of 4.4 wavelengths is shown to have an unshaded sidelobe level of −10.4 dB, which was improved to −14.8 dB when synthesized with a single parameter OF and to −23.1 dB with a multiparameter OF.