  We investigate the form and stability of a cloud of atoms confined in a
harmonic trap when the scattering length is negative. We find that, besides the
known low density metastable solution, a new branch of Bose condensate appears
at higher density when non locality effects in the attractive part are taken
into account. The transition between the two classes of solutions as a function
of the number $N$ of atoms can be either sharp or smooth according to the
strength and range of the attractive interaction. Use of tight traps is
favorable for investigating the evolution of the system as the strength of the
effective interaction increases with $N$.
