In contemporary natural language formalisms like HPSG (Pollard and Sag 1994) the ID/LP format is used to separate the information on dominance from the one on linear precedence thereby allowing significant generalizations on word order. In this paper, we define unification ID/LP grammars. But as mentioned in Seiffert (1991) there are problems concerning the locality of the information determining LP acceptability during parsing. Since one is dealing with partially specified data, the information that is relevant to decide whether the local tree under construction is LP acceptable might be instantiated further during processing. In this paper we propose a modification of the Earley/Shieber algorithm on direct parsing of ID/LP grammars. We extend the items involved to include the relevant underspecified information using it in the completion steps to ensure the acceptability of the resulting structure. Following Sikkel (1993) we define it not as an algorithm, but as a parsing schema to allow the most abstract representation.