Statistical language models (SLMs) for speech recognition have the advantage of robustness, and grammar-based models (GLMs) the advantage that they can be built even when little corpus data is available. A known way to attempt to combine these two methodologies is first to create a GLM, and then use that GLM to generate training data for an SLM. It has however been difficult to evaluate the true utility of the idea, since the corpus data used to create the GLM has not in general been explicitly available. We exploit the Open Source Regulus platform, which supports corpus-based construction of linguistically motivated GLMs, to perform a methodologically sound comparison: the same data is used both to create an SLM directly, and also to create a GLM, which is then used to generate data to train an SLM. An evaluation on a medium-vocabulary task showed that the indirect method of constructing the SLM is in fact only marginally better than the direct one. The method used to create the training data is critical, with PCFG generation heavily outscoring CFG generation.