This paper shows how to improve Hidden Conditional Random Fields (HCRFs) for phone classification by applying various speaker adaptation techniques. These include Maximum A Posteriori (MAP) adaptation as well as a new technique we introduce called Maximum Conditional Likelihood Linear Regression (MCLLR), a discriminative variant of the widely used MLLR algorithm. In previous work, we and others have shown that HCRFs outperform even discriminatively trained HMMs. In this paper we show that HCRFs adapted via MCLLR or via MAP adaptation also work better than similarly adapted HMMs. We also compare MCLLR and MAP adaptation performance with different amounts of adaptation data. MCLLR adaptation performs better when the amount of adaptation data is relatively small, while MAP adaptation outperforms MCLLR with larger amounts of adaptation.