We investigate a technique to adapt unsupervised word embeddings to specific applications, when only small and noisy labeled datasets are available. Current methods use pre-trained embeddings to initialize model parameters, and then use the labeled data to tailor them for the intended task. However, this approach is prone to overfitting when the training is performed with scarce and noisy data. To overcome this issue, we use the supervised data to find an embedding subspace that fits the task complexity. All the word representations are adapted through a projection into this task-specific subspace, even if they do not occur on the labeled dataset. This approach was recently used in the SemEval 2015 Twitter sentiment analysis challenge, attaining state-of-the-art results. Here we show results improving those of the challenge, as well as additional experiments in a Twitter Part-Of-Speech tagging task.