This paper examines two-stage multi-attribute decision strategies in different condi- tions where numbers of alternatives, and attributes are varied. A Monte-Carlo com- puter simulation using the concept of elementary information processes identified de- cision strategies that approximate the accuracy of normative procedures while saving cognitive effort in the two-stage decision making process. The elementary strategies examined in the simulation were nine decision strategies: lexicographic, lexicographic semi-order, elimination by aspect, conjunctive, disjunctive, weighted additive, equally weighted additive, additive difference, and majority of confirming dimensions strategies. Elementary information process and relative accuracy were computed for all combina- tion of two decision strategies for two-phased decision making process. The result of the computer simulation suggested that comparatively effortless and accurate heuristic was the two-phased strategy that used lexicographic strategy to eliminate until a few alternatives in the first stage and used weighted additive strategy in the second stage. Lastly, theoretical and practical implications of this study were discussed.