We propose two new members of the mullite-type family, SnAlBO4 and SnGaBO4, and carry out an in-depth study of their crystal properties using the hybrid method PW1PW. Both are isostructural to PbMBO4 (M = Fe, Mn, Al, Ga), which show axial negative linear compressibility (ANLC), among other interesting features. We find that, although Sn2+ is susceptible of being oxidized by oxygen, a suitable range of experimental parameters exists in which the compounds could be synthesized. We observe absence of ANLC below 20 GPa and explain it by the small space occupied by the lone electron pairs, as indicated by the small length of the corresponding Liebau Density Vectors. In agreement with this fact, the structures present a low number of negative mode-Grüneisen parameters, which may also suggest lack of negative thermal expansion. The electronic properties show a remarkable anisotropic behaviour, with a strong dependence of the absorption spectra on light polarization direction.