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Discrete decision problems with a large number of criteria (as compared to the number of alternatives) present specific difficulties, for example, most of decision alternatives tend to be Pareto-nondominated, some criteria might have binary character, etc. For these reasons, classical methods such as weighted sum aggregation or full utility elicitation are barely applicable for such problems. Methods that might be applied include reference point approaches, particularly if appropriately modified, equitable aggregation approaches and special hierarchical aggregation schemes. The paper presents descriptions and necessary modifications of such methods, together with associated concepts of objective versus subjective decision selection, compensatory versus non-compensatory criteria, preservation of Pareto-nondominance in hierarchical aggregation, etc. Examples show that methods effective in most difficult cases are based on reference point approaches combined with equitable aggregation and objective decision selection.