Multilingual contextual embeddings, such as multilingual BERT and XLM-RoBERTa, have proved useful for many multi-lingual tasks. Previous work probed the cross-linguality of the representations indirectly using zero-shot transfer learning on morphological and syntactic tasks. We instead investigate the languageneutrality of multilingual contextual embeddings directly and with respect to lexical semantics. Our results show that contextual embeddings are more language-neutral and, in general, more informative than aligned static word-type embeddings, which are explicitly trained for language neutrality. Contextual embeddings are still only moderately languageneutral by default, so we propose two simple methods for achieving stronger language neutrality: first, by unsupervised centering of the representation for each language and second, by fitting an explicit projection on small parallel data. Besides, we show how to reach stateof-the-art accuracy on language identification and match the performance of statistical methods for word alignment of parallel sentences without using parallel data.