This paper examines efficient predictive broadcoverage parsing without dynamic programming. In contrast to bottom-up methods, depth-first top-down parsing produces partial parses that are fully connected trees spanning the entire left context, from which any kind of non-local dependency or partial semantic interpretation can in principle be read. We contrast two predictive parsing approaches, topdown and left-corner parsing, and find both to be viable. In addition, we find that enhancement with non-local information not only improves parser accuracy, but also substantially improves the search efficiency.