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Lens-axicon doublets have been used to produce Bessel-Gaussian beams, a narrow non-diffracting beam of relatively constant width. One problem of using Bessel-Gaussian beams is that there is a compromise between achieving a long effective focal length with a small central core radius and distributing the beam intensity between the central core and the off-axis rings. Here, we explore the advantage of tuning the lens-axicon separation, which allows us to have an additional degree of freedom to tailor the beam profile. Moreover, the separation between the lens and the axicon reduces the spherical aberrations in the beam profile, which can then be modeled within the paraxial regime. We study the detrimental effects of the spherical aberrations and provide several options to minimize them. We examine both sharp and shallow axicons used in combination with different converging lenses. We perform a series of detailed experiments to image the structure of the beam through the Bessel region. The spatial light distribution of the lens-axicon system is analyzed by using high dynamic range imaging and complemented with consistent theoretical calculations within the paraxial regime.