  We study the localization length of a pair of two attractively bound
particles moving in a one-dimensional random potential. We show in which way it
depends on the interaction potential between the constituents of this composite
particle. For a pair with many bound states N the localization length is
proportional to N, independently of the form of the two particle interaction.
For the case of two bound states we present an exact solution for the
corresponding Fokker-Planck equation and demonstrate that the localization
length depends sensitively on the shape of the interaction potential and the
symmetry of the bound state wave functions.
