Abstract. Causal sufficiency is a cornerstone assumption in causal discovery. It is, however, not only unlikely to hold in practice but also unverifiable. When it does not hold, existing methods struggle to return meaningful results. In this paper, we show how to discover a causal network over both observed variables and their hidden confounders. Moreover, we extend the algorithmic Markov condition to include latent confounders. In particular, we show that the model becomes identifiable in the linear Gaussian case. We propose a consistent score based on the Minimum Description Length principle to discover the full causal network. Based on this score, we develop an effective algorithm that finds those sets of nodes for which the addition of a confounding factor Z is most beneficial, then fits a new causal network over both observed as well as inferred variables.