We obtain the supergravity solution which describes a bound state of D-string/anti-D-string pairs attached to different fixed planes of an orbifold, in type IIB string theory compactified on T^4/Z_2. For parameters at which the conformal field theory point of view predicts stability, the solution displays a repulson-like singularity. However, we observe that a D-string/anti-D-string pair probe in this background becomes tensionless before reaching the singularity, suggesting a resolution by the

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... enhancon mechanism. Moreover, the force feels by this probe is attractive, in contrast to the repulsive behaviour observed in the non-BPS D-brane description.