SQL queries are optimized to operate directly on compressed data (and obtain the correct result) rather than requiring that the data be first decompressed prior to processing a query. Certain characteristic pattern trees are mapped against a logical input query plan that includes certain logical operators such as a DECOMPRESS that precedes a JOIN or a GROUPBY in association with a COUNT to identify instances in the plan that match a characteristic pattern. Upon locating a match, the input query plan is transformed into a logically equivalent plan that operates correctly on compressed data, by analyzing the interplay of the semantics of logical query operations with the compressed data and substituting less costly structures and operations. DECOMPRESS operations are moved to operate subsequent to a JOIN or eliminated altogether, and COUNT operations are replaced by a different operation, such as SUM, that is logically equivalent for compressed data.