We consider conditions under which the representation of the world available to a boundedly rational decision-maker, whose awareness in- creases over time, constitutes an adequate "small world" (in the sense of Savage 1954) for the assessment of a given decision. Equivalently, we consider whether boundedly rational decision-makers who gradu- ally become aware of all relevant contingencies, can pursue a strategy that is sequentially consistent. We derive conditions on beliefs and preferences that yield a separation between the set of propositions of which the boundedly rational decision-maker is aware and those of which she is unaware and show that these conditions are sufficient to ensure sequential consistency.