The effective elastic contact modulus and the work of adhesion are crucial material parameters needed for the application of theories of adhesive contact to various problems of modern nanotechnology. It is quite common that these parameters are identified using two different kinds of depth-sensing indentation (DSI) tests; in particular, the elastic characteristics are evaluated using indentation that involves the use of a sharp indenter, whereas the work of adhesion is estimated from a series of the DSI tests in which a spherical indenter is used. It can be argued, however, that the customary approaches have various drawbacks. In 2008, Borodich and Galanov showed that these material properties of primary interest may be identified from a single test using a new approach named the BG (Borodich-Galanov) method. The BG method is based on an inverse analysis of a stable region of the dimensionless force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. The method employs the established theories of adhesive indentation, mainly the JKR theory. The BG method was then extended in 2019 by Perepelkin and Borodich (the eBG method) by introducing new approaches to the processing of experimental data and a different objective functional for data fitting. In the present work, some theoretical aspects of the BG and eBG methods are discussed. It is shown that both the BG and eBG methods are simple and robust.