Latent-variable PCFGs (L-PCFGs) are a highly successful model for natural language parsing. Recent work (Cohen et al., 2012) has introduced a spectral algorithm for parameter estimation of L-PCFGs, which - unlike the EM algorithm - is guaranteed to give consistent parameter estimates (it has PAC-style guarantees of sample complexity). This paper describes experiments using the spectral algorithm. We show that the algorithm provides models with the same accuracy as EM, but is an order of magnitude more efficient. We describe a number of key steps used to obtain this level of performance; these should be relevant to other work on the application of spectral learning algorithms. We view our results as strong empirical evidence for the viability of spectral methods as an alternative to EM.