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A numerical optimization study of minimum-fuel Earth-based orbital transfers from low-Earth orbit (LEO) to either medium-Earth orbit (MEO), high-Earth orbit (HEO), or geostationary orbit (GEO), is performed. Various values of maximum allowable thrust acceleration are considered for each type of transfer (LEO-to-MEO, LEO-to-HEO, or LEO-to-GEO). A key aspect of the study performed in this paper is that the optimal thrusting structure is not assumed to be known a priori, but is determined as part of the solution process. In order to determine the optimal thrusting structure, a recently developed bang-bang and singular optimal control (BBSOC) method is employed together with multiple-domain Legendre-Gauss-Radau quadrature collocation. Key results obtained in this study include not only the number of switches in