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Here, we describe two ways to improve the cross-section shape of those tracks by an example of stillwellite-like LaBGeO5 tracks in lanthanum borogermanate glass. Application of the Laguerre-Gaussian beam (LG01 mode) providing different temperature profile and smaller temperature gradients in glass as compared to the conventional Gaussian beam is shown to avoid the effect of the bilateral growth and to form an oblong cross-section of the track with the improved aspect ratio. Recently, we have suggested a method of femtosecond laser-induced amorphization of the laser-written LaBGeO5 crystalline track in lanthanum borogermanate glass [2]. Now, we report a technique for partial laser-induced amorphization of LaBGeO5 tracks which transforms an elongated cross-section of the track into a smaller, nearly circular one. The effect of the helical and sinusoidal trajectories of the amorphizing beam is compared.