Correlation-dependent derivatives, such as asset-backed securities and collateralized debt obligations (CDOs), are common tools for offsetting credit risk. Factor models in the conditional independence framework are widely used in practice to capture the correlated default events of the underlying obligors. An essential part of these models is the accurate and efficient evaluation of the expected loss of the specified tranche, conditional on a given value of a systematic factor (or values of a set of systematic factors). Unlike papers that focus on how to evaluate the loss distribution of the underlying pool, in this paper we focus on the tranche loss function itself. It is approximated by a sum of exponentials so that the conditional expectation can be evaluated in closed form without having to evaluate the pool loss distribution. As an example, we apply this approach to synthetic CDO pricing. Numerical results show that it is efficient.