For multielement antenna arrays (MAA) the desired characteristics of the corresponding pattern are often provided by means of the proper selection or optimization (synthesis) of an apodization function (AF), i.e. an amplitude distribution represented in a sampled manner [1]. However, for some types of MAA not all the known apodization functions (also called weighting windows for digital signal processing applications) [2] can be implemented. The reasons are the constructive and technological restrictions. They are originated by different factors depending upon the type of MAA under consideration. In particular, for wave-guide-slot antennas the desirable amplitude distribution is provided by means of varied displacement of slots in the wide wall of waveguide in respect to its axis. In this case the minimal distance of the slot to the axis is not less than some value predetermined by geometrical dimensions of the slots, wavelength and the requirements to antenna solidity [3]. Similar reasons take place for patch MAAs. In general, the factors mentioned above lead to restricting an available range of apodization function value variation. If it is represented in a normalized way then AF values can not be less than typically 0.1–0.2. That is why below we consider several possible solutions applicable for described constructive technological restrictions. In addition, we propose some new AFs having rather good characteristics of the corresponding patterns.