In this article, we compare publication and citation coverage of the new Microsoft Academic with all other major sources for bibliometric data: Google Scholar, Scopus, and the Web of Science, using a sample of 145 academics in five broad disciplinary areas: Life Sciences, Sciences, Engineering, Social Sciences, and Humanities. When using the more conservative linked citation counts for Microsoft Academic, this data-source provides higher citation counts than both Scopus and the Web of Science for Engineering, the Social Sciences, and the Humanities, whereas citation counts for the Life Sciences and the Sciences are fairly similar across these three databases. Google Scholar still reports the highest citation counts for all disciplines. When using the more liberal estimated citation counts for Microsoft Academic, its average citations counts are higher than both Scopus and the Web of Science for all disciplines. For the Life Sciences, Microsoft Academic estimated citation counts are higher even than Google Scholar counts, whereas for the Sciences they are almost identical. For Engineering, Microsoft Academic estimated citation counts are 14% lower than Google Scholar citation counts, whereas for the Social Sciences this is 23%. Only for the Humanities are they substantially (69%) lower than Google Scholar citations counts. Overall, this first large-scale comparative study suggests that the new incarnation of Microsoft Academic presents us with an excellent alternative for citation analysis. We therefore conclude that the Microsoft Academic Phoenix is undeniably growing wings; it might be ready to fly off and start its adult life in the field of research evaluation soon.