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Solutions of a rigid polyelectrolyte molecule, sulfo-poly(phenyleneterephthalamide) (SPTTA), in deuterated water have been investigated using small-angle neutron scattering. At low concentrations (1 wt%) the scattering spectrum presents a soft maximum similar to that of the interaction of rod-like objects. Two counterions are used, H+ and Li+, and it is shown that aggregation is favoured as the proportion of Li+ counterions increases. When kept at rest at room temperature, the solutions exhibit spontaneous birefringence. A 1 wt% solution was investigated under shear and it is shown that a very small shear rate is needed to produce a very strong alignment of rod-like objects. Such alignment saturates at high shear rates. Upon cessation of shear, a very long relaxation time is observed. The set of results strongly suggest aggregation of rigid polyelectrolyte molecules into long needles exhibiting very small cross sections.