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Rectangular and complex-shaped absorbing elements based on a uniform resistive film are used for constructing waveguide, coaxial, and microstrip attenuators. A decrease in the attenuator's dimensions leads to difficulties in the implementation of low and high attenuations, which requires passing to absorbing elements based on piecewise uniform structures. In this work, topologies of small absorbing elements of the waveguide, coaxial, and microstrip attenuators are proposed to implement a wide range of radio signal power attenuations. They differ from the known elements of attenuators with a two-layer resistive film in terms of their lower temperature stability and sophisticated manufacturing technology. Such attenuation is achieved by using a single-layer resistive film with a central region having a high (cut) or low (conductor) specific resistance. A technique based on the rigorous method of conformal mappings for calculating the proposed absorbing elements is developed. In the considered particular cases, the obtained relations coincide with those known in the literature. Three-dimensional plots of radio signal power attenuation and normalized input resistance as functions of the normalized size of the cut or conductor of the central region are presented. A broad range of possibilities of the control for output parameters of absorbing elements are outlined. The working capacity of the technique is verified by modeling both the equivalent circuit parameters and output parameters of the absorbing elements, namely, input resistance and attenuation, as well as by the analysis of real samples of small add-on absorbing elements of microstrip attenuators with the proposed topologies. The modeling is carried out in the Russian Elcut software package. [ABSTRACT FROM AUTHOR]