Summary: A book embedding of a graph consists of a linear ordering of the vertices along a line in 3-space (the spine) and an assignment of edges to half-planes with the spine as boundary (the pages) so that edges assigned to the same page can be drawn on that page without crossings. Given a graph \(G=(V,E)\), let \(f:V\to\mathbb{N}\) be a function such that \(1\leq f(v)\leq\deg(v)\). We present a Las Vegas algorithm which produces a book embedding of \(G\) with \(O(\sqrt{| E | \cdot\max_v\lceil \deg(v)/f(v) \rceil})\) pages such that at most \(f(v)\) edges incident to a vertex \(v\) are on a single page. This result generalises that of \textit{S. M. Malitz} [J. Algorithms 17, 71--84 (1994; Zbl 0810.68102)].