Linear mixed models are frequently overparameterized. A primary source of this problem are correlation parameters. Often these correlation parameters do not contribute to goodness of model fit (i.e., there is not enough evidence that they differ significantly from zero). The new double-bar syntax allows a convenient specification of zero-correlation-parameter linear mixed models in lmer().
Paper: Yan, M., Zhou, W., Shu, H., Yusupu, R., Miao, D., Kruegel, A., & Kliegl, R. (2014). Eye Movements Guided by Morphological Structure: Evidence from the uighur Language. Cognition, 132 (2), 181-215. URL: http://www.sciencedirect.com/science/article/pii/S001002771400047X Script is based on uighur_package.v2.R (available on Potsdam Mind Research Repository, also a preprint of the paper); see this script for details about computation of various derived variables (e.g., centering for LMMs, grouping for figures)