  We determine the leading shift of the Bose-Einstein condensation temperature
for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by
treating both a Gaussian and a Lorentzian spatial correlation for the quenched
disorder potential. Increasing the correlation length from values much smaller
than the geometric mean of the trap scale and the mean particle distance to
much larger values leads first to an increase of the positive shift to a
maximum at this critical length scale and then to a decrease.
