  We investigate theoretically an original route to achieve Bose-Einstein
condensation using dark power-law laser traps. We propose to create such traps
with two crossing blue-detuned Laguerre-Gaussian optical beams. Controlling
their azimuthal order $\ell$ allows for the exploration of a multitude of
power-law trapping situations in one, two and three dimensions, ranging from
the usual harmonic trap to an almost square-well potential, in which a
quasi-homogeneous Bose gas can be formed. The usual cigar-shaped and
disk-shaped Bose-Einstein condensates obtained in a 1D or 2D harmonic trap take
the generic form of a "finger" or of a "hockey puck" in such Laguerre-Gaussian
traps. In addition, for a fixed atom number, higher transition temperatures are
obtained in such configurations when compared with a harmonic trap of same
volume. This effect, which results in a substantial acceleration of the
condensation dynamics, requires a better but still reasonable focusing of the
Laguerre-Gaussian beams.
