This paper discusses a new approach to the problem of dividing the text of a paragraph into lines of approximately equal length. Instead of simply making decisions one line at a time, the method considers the paragraph as a whole, so that the final appearance of a given line might be influenced by the text on succeeding lines. A system based on three simple primitive concepts called ‘boxes’, ‘glue’, and ‘penalties’ provides the ability to deal satisfactorily with a wide variety of typesetting problems in a unified framework, using a single algorithm that determines optimum breakpoints. The algorithm avoids backtracking by a judicious use of the techniques of dynamic programming. Extensive computational experience confirms that the approach is both efficient and effective in producing high-quality output. The paper concludes with a brief history of line-breaking methods, and an appendix presents a simplified algorithm that requires comparatively few resources.