  We develop a procedure to modify the correlations of a speckle potential.
This procedure, that is suitable for spatial light modulator devices, allows
one to increase the localization efficiency of the speckle in a narrow energy
region whose position can be easily tuned. This peculiar energy-dependent
localization behavior is explored by pulling the potential through a
cigar-shaped Bose-Einstein condensate. We show that the percentage of dragged
atoms as a function of the pulling velocity depends on the potential
correlations below a threshold of the disorder strength. Above this threshold,
interference effects are no longer clearly observable during the condensate
drag.
