A procedure for decision-making under risk is developed and axiomatized. It provides another explanation for the Allais paradox as well as justification for some other preference patterns that can not be represented by the expected utility model, but it includes expected utility representation fo preferences as a particular case. The idea of the procedure is that evaluation of the lotteries takes two steps. First, a decision maker classifies a lottery as a "bad," "good" or "medium" one. Then comparing the lotteries the decision maker uses lexicographic ordering between the classes and expected utility value (with possibly different utility scales for different classes) within each of the three categories. The paper contains comparison of the suggested procedure with several other non-expected utility models. Many preference patterns that motivated the other models can be explained within the suggested procdedure. Key Words: threshold, expected utility, Allais paradox.