This paper addresses the task of nuisance reduction in two-wire speaker recognition applications. Besides channel mismatch, two-wire conversations are contaminated by extraneous speakers which represent an additional source of noise in the supervector domain. It is shown that two-wire nuisance manifests itself as undesirable directions in the inter-speaker subspace. For this purpose, we derive two alternative Nuisance Attribute Projection (NAP) formulations tailored for two-wire sessions. The first formulation generalizes the NAP framework based on a model of two-wire conversations. The second formulation explicitly models the fourvs. two-wire supervector variability. Preliminary experiments show that two-wire NAP significantly outperforms regular NAP in varied two-wire tasks.