We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs). Each of these methods combines weighted model counting (WMC) with constraint satisfaction and optimisation. They use knowledge compilation to address the model counting problem; subsequently, either a constraint programming (CP) solver or mixed integer programming (MIP) solver is used to solve the overall SCP. We first explore a method that is generic and decomposes constraints on probability distributions into a multitude of smaller, local constraints. For the second method, we show that many probability distributions in real-world SCPs have a monotonic property, and how to exploit that property to develop a global constraint. We discuss theoretical (dis)advantages of each method, with a focus on methods that employ ordered binary decision diagrams (OBDDs) to encode the probability distributions, and then evaluate their performances experimentally. To configure the space of parameters of these approaches, we propose to use the framework of programming by optimisation (PbO). The results show that a CP-based pipeline obtains the best performance on well-known data mining and frequent itemset mining problems.