High-resolution (0.01 cm(-1)) FTIR spectra of AI(BH4)(3) and AI(BD4)(3) recorded for low-pressure samples at room temperature are presented that show only broad vibrational bands, with no trace of resolved rotational structure. The BH bridge stretching and the BH2 deformation regions were also examined at 0.001 cm(-1) resolution by tunable infrared diode laser spectroscopy for samples cooled to similar to 10 K in a multipass, slit expansion. These too show near continua, with much more congestion than predicted by nonrigid rotor simulations based on boron isotopic shifts, Coriolis constants, and centrifugal distortion parameters estimated from ab initio calculations. The latter indicate that a particularly low barrier, corresponding to the prismatic D-3h structure, separates two equivalent, lower energy D-3 forms in which the BH4 units are rotated 23 degrees about the Al-B axes. The potential energy surface for the relevant conrotary torsional coordinate is examined at the CCSD/6-311G**//MP2/6-311G** level, yielding a barrier height of 490 cm(-1) and v = 0 and 1 level splittings of 0.052 and 2.7 cm(-1), respectively. The extreme spectral congestion observed is believed to arise primarily from splittings of the ground state and the upper vibrational levels of modes that couple to this conrotary torsional motion and to other tumbling modes of the BH4 units.