Our recently proposed method for automatic detection, calibration and evaluation of Debye-Scherrer ellipses using pattern-recognition techniques and advanced signal filtering was applied to the two-dimensional powder diffraction data of the non-ferroelectric, non-centrosymmetric non-linear optical (NLO) compound alpha-BiB(3)O(6) as a function of pressure. At ambient conditions, alpha-BiB(3)O(6) crystallizes in the space group C2 (phase I). In the pressure range between P = 6.09 and 6.86 GPa, it exhibits a first-order phase transition into a structure with the space group C1 (P1) [phase II at P = 8.34 GPa: a = 7.4781 (6), b = 3.9340 (4), c = 6.2321 (6) A, alpha = 93.73 (1), beta = 102.93 (1), gamma = 90.76 (1) degrees , and V = 178.24 (3) A(3)]. Non-linear compression behaviour over the entire pressure range is observed, which can be described by two Vinet relations in the ranges from P = 0.0 to 6.09 GPa, and from P = 6.86 to 11.6 GPa. The extrapolated bulk moduli of the high-pressure phases were determined to be K(0) = 38 (1) GPa for phase I, and K(0) = 114 (10) GPa for phase II. The crystal structures of both phases were refined against X-ray powder diffraction data measured at several pressures between 0.0 and 11.6 GPa. The structural phase transition of alpha-BiB(3)O(6) is mainly characterized by a reorientation of the [BO(3)](3-) triangles, the [BO(4)](5-) tetrahedra and the lone electron pair which is localized at Bi(3+), in order to optimize crystal packing.