We present a dual decomposition framework for multi-document summarization, using a model that jointly extracts and compresses sentences. Compared with previous work based on integer linear programming, our approach does not require external solvers, is significantly faster, and is modular in the three qualities a summary should have: conciseness, informativeness, and grammaticality. In addition, we propose a multi-task learning framework to take advantage of existing data for extractive summarization and sentence compression. Experiments in the TAC-2008 dataset yield the highest published ROUGE scores to date, with runtimes that rival those of extractive summarizers.