Max independent set is a paradigmatic problem in theoretical computer science and numerous studies tackle its resolution by exact algorithms with non-trivial worst-case com- plexity, both in the general case and in the case of bounded degree graphs. Here, we improve several of these results. We first get an algorithm in O* (1.0854n) for graphs of average de- gree 3 based upon a detailed case analysis using several reduction rules. Then we propose a generic method showing how improvement of the worst-case complexity for max independent set in graphs of average degree d entails improvement of it in any graph of average degree greater than d and, based upon it, we tackle max independent set by improving its complexity in graphs of average degree 4, 5 and 6. Finally, we combine this method with measure and conquer techniques to get improved running times for general graphs. The best computation bounds obtained are O* (1.1571n), O* (1.1918n) and O *(1.2070n), for graphs of maximum degree 4, 5 and 6 respectively, and mainly, O* (1.2125n) for general graphs. These results improve upon the best known results for these cases.