Tight upper bounds for the expected loss of the DEBA (Deterministic-Elimination-By-Aspects) lexicographic selection heuristic are obtained for the case of an additive separable utility function with unknown non-negative, non-increasing attribute weights for numbers of alternatives and attributes as large as 10 under two probabilistic models: one in which attributes are assumed to be independent Bernouilli random variables and another one with positive inter-attribute correlation. The upper bounds improve substantially previous bounds and extend significantly the cases in which a good performance of DEBA can be guaranteed under the assumed cognitive limitations.