We present a novel algorithm for surface realisation with lexicalist grammars. In this algorithm, the structure of the input is used both top-down to constrain the selection of applicable rules and bottom-up to filter the initial search space associated with local input trees. In addition, parallelism is used to recursively pursue the realisation of each daughter node in the input tree. We evaluate the algorithm on the input data provided by the Generation Challenge Surface Realisation Task and show that it drastically reduce processing time when compared with a simpler, top-down driven, lexicalist approach.