The energy spectra of a sparse ensemble of electrons scattered by relativistically intense laser pulses are studied numerically by solving the relativistic Newton equations with the Lorentz force generated by an electromagnetic envelope in vacuum. The expressions for the envelope describe focused optical fields, include significant short-pulse corrections, and afford the representation of laser radiation with various types of transverse distributions of amplitude. The dependence of the character of the electron energy spectra on the type of the transverse distribution of laser amplitude is explored. For Gaussian pulses, the electron energy spectra within specific angular ranges tend to either include a relativistic maximum while being localized around it or to have the shapes of evanescent distributions dominated by the cold component. Conversely, the energy spectra of electrons ejected into certain angular ranges by laser pulses having first-order Laguerre profiles combine pronounced cold components and structured strongly relativistic features. The presumed laser pulse transverse structure and the shapes of the calculated electron energy spectra for first-order Laguerre amplitude distributions are shown to match, qualitatively, those reported in a recent experimental study by Kalashnikov et al. in 2015, which revealed the electron energy spectra spanning both the sub-relativistic and the markedly relativistic energy domains.
