Future galaxy surveys of the large-scale structure in the Universe will provide a wealth of new data and make it possible to use higher-order statistics beyond the power spectrum, such as the bispectrum (or 3-point correlation function), to constrain galaxy clustering, the standard LCDM cosmology, and many of its possible extensions. However, it may be possible and preferable to use recently devised alternative statistics, such as the line correlation function or position-dependent power spectrum, to recover most of the information contained within the bispectrum while avoiding a more challenging bispectrum analysis. I will present work in which we have used N-body simulations and theoretical models for the clustering of dark matter to predict whether these alternate statistics can constrain a basic set of cosmological parameters as strongly as the bispectrum. Weighing the relative constraining power of these competing statistics will shed more light on how complementary observations from upcoming galaxy surveys will be, and inform more efficient, robust ways of analyzing future data sets.