The field of tumor phylogenetics focuses on studying the differences within cancer cell populations. Many efforts are done within the scientific community to build cancer progression models trying to understand the heterogeneity of such diseases. These models are highly dependent on the kind of data used for their construction, therefore, as the experimental technologies evolve, it is of major importance to exploit their peculiarities. In this work we describe a cancer progression model based on Single Cell DNA Sequencing data. When constructing the model, we focus on tailoring the formalism on the specificity of the data. We operate by defining a minimal set of assumptions needed to reconstruct a flexible DAG structured model, capable of identifying progression beyond the limitation of the infinite site assumption. Our proposal is conservative in the sense that we aim to neither discard nor infer knowledge which is not represented in the data. We provide simulations and analytical results to show the features of our model, test it on real data, show how it can be integrated with other approaches to cope with input noise. Moreover, our framework can be exploited to produce simulated data that follows our theoretical assumptions. Finally, we provide an open source R implementation of our approach, called CIMICE, that is publicly available on BioConductor.