The atomic structure of BiSe was redetermined to ascertain the structural features of this layered material and to carry out band structure analyses on the BixSey phases. BiSe crystallizes in trigonal symmetry (space group ml) with a = 4.212(1)Angstrom, c = 22.942(8)Angstrom, V = 352.5(2)Angstrom(3), and Z = 6. The structure determination conducted from 191 reflections [I greater than or equal to 3 sigma(I)] and 22 variables led to a reliability factor of R = 2.42% and R(w) = 2.50%. Some Bi<->Se substitutional disorder is revealed and some clues for similar disorder in BiTe phase are given. Apart from the disorder, BiSe structural features are in good agreement with those previously reported. In particular, atomic distances match those found in parent Bi2Se3 and Bi4Se3 phases. The BiSe structure is built up from two Se-Bi-Se-Bi-Se (5) and one Bi-Bi (2) slabs. Van der Waals contacts only exist between adjacent (5) slabs, thus making BiSe a true 2D material (like Bi2Se3 and contrary to Bi4Se3). Band structure calculations confirm the absence of anionic bonding between selenium atoms and predict good conductivity within the layers. From a Mulliken population analysis, an oxidation stare balance could be proposed for all BixSey phases and for the BixTey compounds alike, e.g. Bi-0(Bi-III)(2)(Se--II)(3) and (Bi-0)(2)(Bi-III)(2)(Se--II)(3) for BiSe and Bi4Se3, respectively. Starting with Bi-III and Se--II ions in Bi2Se3, the adding of zerovalent Bi-Bi slabs does not change the pristine charge balance and, thus, explains the formation of all the BixSey compounds observed to date.