Self-shadowing precision problem.

I have implemented shadow mapping, all works fine except that self-shadows are not rendered correctly, as you can see in the picture:

The problem looks like z-fighting, does anybody know how I can solve it?

Here my lookup function:

float lookup( )
    float shadow;
    float depth = texture( shadowMap, ShadowCoord.xy ).x;

    shadow = ShadowCoord.z > depth ? 0.25f : 1.0f;

    return shadow;

Thanks in advance