The interest in individuals’ non-strictly rational behaviour has permeated into discrete choice models pushed by several psychological theories. We analysed Satisficing Theory, which is particularly useful when decision makers have to face the cognitive burden of complex decisions. Three principles of the theory are discussed noting that the third, partial pay-off functions, has not been addressed in the literature. We implement the three principles mathematically obtaining a discrete choice model in which the decision maker chooses the first satisfactory alternative. The model formulation is analytically derived, as well as its properties. The Stochastic Satisficing model allows variable or constant marginal rates of substitution and enables the explicit characterization of non-compensatory behaviours. The model can also explain attribute saturation and non-attendance of high order needs when basic needs are not fulfilled. We analysed the model performance on synthetic data, showing that it is likely to be unbiased and consistent for relatively common samples sizes. When tested on real data, the model proves its flexibility to also adapt to constant marginal rates of substitution. We conclude that the model is a good characterization of Satisficing behaviour for simple datasets.