Drawing outer-1-planar graphs revisited Vol. 26, no. 1, pp. 59-73, 2022. Regular paper. Abstract In a recent article (Auer et al., Algorithmica 2016) it was claimed that every outer-1-planar graph has a planar visibility representation of area $O(n\log n)$. In this paper, we show that this is wrong: There are outer-1-planar graphs that require $\Omega(n^2)$ area in any planar drawing. Then we give a construction (using crossings, but preserving a given outer-1-planar embedding) that results in an orthogonal box-drawing with $O(n\log n)$ area and at most two bends per edge.  This work is licensed under the terms of the CC-BY license. Submitted: September 2020. Reviewed: August 2021. Revised: October 2021. Accepted: December 2021. Final: January 2022. Published: January 2022. Communicated by Michael Kaufmann article (PDF) BibTeX