Connectomics deals with the problem of reconstructing neural circuitry from electron microscopy images at the synaptic level. Automatically reconstructing circuits from these volumes requires high fidelity 3-D instance segmentation, which yet appears to be a daunting task for current computer vision algorithms. Hence, to date, most datasets are not reconstructed by fully-automated methods. Even after painstaking proofreading, these methods still produce numerous small errors. In this paper, we propose an approach to accelerate manual reconstructions by learning to correct imperfect manual annotations. To achieve this, we designed a novel solution for the canonical problem of marker-based 2-D instance segmentation, reporting a new state-of-the-art for region-growing algorithms demonstrated on challenging electron microscopy image stacks. We use our marker-based instance segmentation algorithm to learn to correct all "sloppy"object annotations by reducing and expanding all annotations. Our correction algorithm results in high quality morphological reconstruction (near ground truth quality), while significantly cutting annotation time (~8x) for several examples in connectomics. We demonstrate the accuracy of our approach on public connectomics benchmarks and on a set of large-scale neuron reconstruction problems, including on a new octopus dataset that cannot be automatically segmented at scale by existing algorithms.