In this paper we propose a mathematical model for imprecise probability representing an agent’s uncertain beliefs. The proposed model is closely related to the credal set model, which uses a set of probability functions. The credal set model can be conceived of as encoding judgements such as it seeming more likely that it’ll rain than snow. It requires that these judgements be closed under consequences according to the probability functions that satisfy the judgements. We adopt a similar idea but instead only require her judgements to be closed under finite consequences according the probability functions satisfying them. The formal model that we will provide for this is a collection of probability constraints which is closed under finite intersection and supersets. That is, it forms the mathematical structure of a filter. We will show how this allows the model to avoid some criticisms of the credal set model by Walley which led him to instead arguing for a model of uncertainty as a set of desirable gambles directly. We will show a close connection between this desirable gambles model and the proposed model of probability filters.