Pugh, WilliamWonnacott, DavidStandard array data dependence techniques can only reason about linear constraints. There has also been work on analyzing some dependences involving polynomial constraints. Analyzing array data dependences in real-world programs requires handling many ``unanalyzable'' terms: subscript arrays, run-time tests, function calls. The standard approach to analyzing such programs has been to omit and ignore any constraints that cannot be reasoned about. This is unsound when reasoning about value-based dependences and whether privatization is legal. Also, this prevents us from determining the conditions that must be true to disprove the dependence. These conditions could be checked by a run-time test or verified by a programmer or aggressive, demand-driven interprocedural analysis. We describe a solution to these problems. Our solution makes our system sound and more accurate for analyzing value-based dependences and derives conditions that can be used to disprove dependences. We also give some preliminary results from applying our techniques to programs from the Perfect benchmark suite. (Also cross-referenced as UMIACS-TR-94-123)en-USTechnical Report