  This paper is concerned with the long wavelength instabilities (infrared
catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the
modulational instability in ``cigar-shaped'' (1D) attractive BECs and the
transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We
suggest mechanisms, and give explicit estimates, on how to ``engineer'' the
trapping conditions of the condensate to avoid such instabilities: the main
result being that a tight enough trapping potential suppresses the
instabilities present in the homogeneous limit. We compare the obtained
estimates with numerical results and we highlight the relevant regimes of
dynamical behavior.

Soft Condensed Matter