The focus of the 2010 NIST Speaker Recognition Evaluation (SRE) was the low false alarm regime of the detection error trade-off (DET) curve. This paper presents several approaches that specifically target this issue. It begins by highlighting the main problem with operating in the low-false alarm regime. Two sets of methods to tackle this issue are presented that require a large and diverse impostor set: the first set penalizes trials whose enrollment and test utterances are not nearest neighbors of each other while the second takes an adaptive score normalization approach similar to TopNorm and ATNorm.