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When analyzing eye movement data from the reading of multi-line texts, it is important to ensure that fixations are assigned correctly to the lines of the text. This is a non-trivial problem as eye movement data are noisy and often show complex non-linear distortions. Here, we introduced Slice, a new algorithm to assign fixations in multi-line text. We describe how Slice operates and evaluate it using a data set of natural reading data. Results show that Slice performs better than the default method used by many software packages, is robust to many forms of distortions, and approximates manual coding decisions.