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Cross-lingual sentence encoders (CLSE) create fixed-size sentence representations with aligned translations. Current pre-trained CLSE approaches use sentence-level objectives only. This can lead to loss of information, especially for tokens, which then degrades the sentence representation. We propose MEXMA, a novel approach that integrates both sentence-level and token-level objectives. The sentence representation in one language is used to predict masked tokens in another language, with both the sentence representation and *all tokens directly update the encoder*. We show that adding token-level objectives greatly improves the sentence representation quality across several tasks. Our approach outperforms current pre-trained cross-lingual sentence encoders on bitext mining as well as several downstream tasks. We also analyse the information encoded in our tokens, and how the sentence representation is built from them.