Novel neural models have been proposed in recent years for learning under domain shift. Most models, however, only evaluate on a single task, on proprietary datasets, or compare to weak baselines, which makes comparison of models difficult. In this paper, we re-evaluate classic general-purpose bootstrapping approaches in the context of neural networks under domain shifts vs. recent neural approaches and propose a novel multi-task tri-training method that reduces the time and space complexity of classic tri-training. Extensive experiments on two benchmarks for part-of-speech tagging and sentiment analysis are negative: while our novel method establishes a new state-of-the-art for sentiment analysis, it does not fare consistently the best. More importantly, we arrive at the somewhat surprising conclusion that classic tri-training, with some additions, outperforms the state-of-the-art for NLP. Hence classic approaches constitute an important and strong baseline.