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This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra extended by an operation for computing possible answers, a query on the logical level can be translated into, and evaluated as, a single relational algebra query on the U-relational representation. The translation scheme essentially preserves the size of the query in terms of number of operations and, in particular, number of joins. Standard techniques employed in off-the-shelf relational database management systems are effective for optimizing and processing queries on U-relations. In our experiments we show that query evaluation on U-relations scales to large amounts of data with high degrees of uncertainty.