We present theory and experiments in good agreement for ballistic magnetoresistance in nanoscopic-size contacts in 3 d metals (Ni and Co). It is found that values of the ballistic magnetoconductance of  ∼ 300% at room temperature can be explained by scattering by the domain wall which is trapped in the constriction region. These values are obtained for very small contacts and they decrease very fast as the contact size increases. The theory also explains this behavior.