We investigate five different fairness criteria in a simple model of fair resource allocation of indivisible goods based on additive preferences. We show how these criteria are connected to each other, forming an ordered scale that can be used to characterize how conflicting the agents' preferences are: the less conflicting the preferences are, the more demanding criterion this instance will be able to satisfy, and the more satisfactory the allocation will be. We analyze the computational properties of the five criteria, give some experimental results about them, and further investigate a slightly richer model with <math>k</math>-additive preferences.