Translation with pivot languages has recently gained attention as a means to circumvent the data bottleneck of statistical machine translation (SMT). This paper tries to give a mathematically sound formulation of the various approaches presented in the literature and introduces new methods for training alignment models through pivot languages. We present experimental results on Chinese-Spanish translation via English, on a popular traveling domain task. In contrast to previous literature, we report experimental results by using parallel corpora that are either disjoint or overlapped on the pivot language side. Finally, our original method for generating training data through random sampling shows to perform as well as the best methods based on the coupling of translation systems.