A number of researchers have recently conducted experiments comparing “deep” hand-crafted wide-coverage with “shallow” treebank- and machine-learning-based parsers at the level of dependencies, using simple and automatic methods to convert tree output generated by the shallow parsers into dependencies. In this article, we revisit such experiments, this time using sophisticated automatic LFG f-structure annotation methodologies with surprising results. We compare various PCFG and history-based parsers to find a baseline parsing system that fits best into our automatic dependency structure annotation technique. This combined system of syntactic parser and dependency structure annotation is compared to two hand-crafted, deep constraint-based parsers, RASP and XLE. We evaluate using dependency-based gold standards and use the Approximate Randomization Test to test the statistical significance of the results. Our experiments show that machine-learning-based shallow grammars augmented with sophisticated automatic dependency annotation technology outperform hand-crafted, deep, wide-coverage constraint grammars. Currently our best system achieves an f-score of 82.73% against the PARC 700 Dependency Bank, a statistically significant improvement of 2.18% over the most recent results of 80.55% for the hand-crafted LFG grammar and XLE parsing system and an f-score of 80.23% against the CBS 500 Dependency Bank, a statistically significant 3.66% improvement over the 76.57% achieved by the hand-crafted RASP grammar and parsing system.