Abstract. Grounding is the task of reducing a first order formula to ground formula that is equivalent on a given universe, and is important in many kinds of problem solving and reasoning systems. One method for grounding is based on an extension of the relational algebra, exploiting the fact that grounding over a given domain is similar to query answering. In this paper, we introduce two methods for speeding up algebraic grounding by reducing the size of tables produced. One method employs rewriting of the formula before grounding, and the other uses a further extension of the algebra that makes negation efficient. We have implemented the methods, and present experimental evidence of their effectiveness.