This paper presents a new approach to two-level hazard-free sum-of-products logic minimization. No currently available minimizers for single-output literal-exact two-level hazard-free logic minimization can handle large circuits without synthesis times ranging up over thousands of seconds. The logic minimization approach presented in this paper is based on state graph exploration in conjunction with single-cube cover algorithms. Our algorithm achieves fast logic minimization by using compacted state graphs and cover tables and an efficient algorithm for single-output minimization. Our exact two-level hazard-free logic minimizer finds minimal number of literal solutions and is significantly faster than existing literal exact methods--over two orders of magnitude faster for the largest extended burst-mode benchmarks to date. This includes a benchmark that has never been possible to solve exactly in number of literals before.