The difficulties encountered in sequential decision-making problems under uncertainty are often linked to the large size of the state space. Exploiting the structure of the problem, for example by employing a factored representation, is usually an efficient approach but, in the case of partially observable Markov decision processes, the fact that some state variables may be visible has not been sufficiently appreciated. In this article, we present a complementary analysis and discussion about MOMDPs, a formalism that exploits the fact that the state space may be factored in one visible part and one hidden part. Starting from a POMDP description, we dig into the structure of the belief update, value function, and the consequences in value iteration, specifically how classical algorithms can be adapted to this factorization, and demonstrate the resulting benefits through an empirical evaluation.