Using a set of structural models, we evaluate the price of default protection for a sample of US corporations. In contrast to previous evidence from corporate bond data, credit default swap (CDS) premia are not systematically underestimated. In fact, one of our studied models has little difficulty on average in predicting their level. For robustness, we perform the same exercise for bond spreads by the same issuers on the same trading date. As expected, bond spreads relative to the treasury curve are systematically underestimated. This is not the case when the swap curve is used as a benchmark, suggesting that previously documented underestimation results may be sensitive to the choice of risk-free rate.