An improved normalization methodology enabling better optimization of SQL queries is described. The normalization methodology effectively handles three-valued SQL search conditions and operates in reduced memory environments. A query is examined and selectively normalized by examining each segment of the query to determine whether it is advantageous to fully convert that segment to conjunctive normal form (CNF). If full conversion of the segment to CNF is not advantageous, then only the useful conjunctive conditions (prime implicates) that can be derived from the original input are saved. These useful conjuncts (prime implicates) are unioned with the original statement, resulting in a search condition that is semantically equivalent to the original expression, but that can be better exploited by a query optimizer. This enables better optimization of the original query without the system overhead that would result from full normalization of the query.