Research has shown that handset selectors can be used to assist telephone-based speech/speaker recognition. Most handset selectors, however, simply select the most likely handset from a set of known handsets even for speech coming from an ‘unseen’ handset. This paper proposes a divergence-based handset selector with outof- handset (OOH) rejection capability to identify the ‘unseen’ handsets. This is achieved by measuring the Jensen difference between the selector’s output and a constant vector with identical elements. The resulting handset selector is combined with a feature-based channel compensation algorithm for telephone-based speaker verification. Utterances whose handsets were identified as ‘unseen’ are either transformed by a global bias vector or normalized by cepstral mean subtraction (CMS). On the other hand, if the handset can be identified (considered as ‘seen’), its corresponding transformation parameters will be used to transform the utterances. Experiments based on ten handsets of the HTIMIT corpus show that using the transformation parameters of the ‘seen’ handsets to transform the utterances with correctly identified handsets and processing those utterances with ‘unseen’ handsets by CMS achieve the best result.