The paper investigates the use of richer syntactic dependencies in the structured language model (SLM). We present two simple methods of enriching the dependencies in the syntactic parse trees used for initializing the SLM. We evaluate the impact of both methods on the perplexity (PPL) and word-error-rate (WER, N-best rescoring) performance of the SLM. We show that the new model achieves an improvement in PPL and WER over the baseline results reported using the SLM on the UPenn Treebank and Wall Street Journal (WSJ) corpora, respectively.