Despite its simplicity, the popular one-factor Gaussian copula model remains the market standard for the valuation of collateralized debt obligation tranches and nth-to-default trades. However, it suffers from well-known weaknesses, mainly due to the tail behavior of the normal distribution (namely, the tails are too light and there is no tail dependence whatever the copula correlation). Alternative models have been proposed. Among these is the double-t copula, which does not share the drawbacks of the Gaussian copula yet remains relatively uncomplex. In spite of these features, this framework suffers from some technical problems relating to its implementation. Without a lot of care, this technique can easily produce inconsistent results. In our opinion, these difficulties have prevented practitioners from turning a theoretically sound model into a workable pricing tool. This paper aims to fill this gap by giving routes toward a reliable implementation of the double-t copula framework, thereby removing the drawbacks of the framework when compared with the Gaussian one. The first purpose of this paper is to show that the implementation issues related to the double-t model actually reduce to the estimation of integrals with respect to some Student's t distributions. The second part of the paper presents an efficient numerical method to perform this tedious task.