Title: Filtered Semi-Markov CRF. Abstract: Semi-Markov CRF \citep{semicrf} has been proposed as an alternative to the traditional Linear Chain CRF\citep{crf} for text segmentation tasks such as Named Entity Recognition. In contrast to CRF, which treats text segmentation as token-level prediction, Semi-CRF considers spans as the task's basic unit, which makes it more expressive. However, Semi-CRF has two major drawbacks: (1) it has quadratic complexity over sequence length as it operates on every span of the input sequence, and (2) empirically, it performs worse than classical CRF for sequence labeling tasks such as NER. In our work, we propose Filtered Semi-Markov CRF, a Semi-CRF variant that addresses the aforementioned issues. Our model extends Semi-CRF by incorporating a filtering step for eliminating irrelevant segments, which helps in reducing the complexity and allows to dramatically reduce the search space. On a variety of NER benchmarks, we find that our approach outperforms both CRF and Semi-CRF models while being significantly faster. We will make our code available to the public. 