Human solid tumors are believed to have very high mutation rates at least in the early stage of extension. Irrespective of whether the increased mutation rate is a necessary condition for the tumor development or not, extremely high mutation rates such as in excess of the so-called "threshold" would before long result in the natural death of tumor cells. In reality, however, we are dying by cancer. Thus, it has been hypothesized that tumor cells should make a quick transition from the higher mutation state to the lower one. According to our "disparity-mutagenesis model", however, carcinogenesis could continue without any incident even under a prolonged period of high mutation rates. Namely, if lagging-strand-biased mutations far beyond the threshold of mutation rate are introduced in tumor cells, the tumor could progress to malignant extension without extinction. The results of evolution experiments using mutator microorganisms are discussed in terms of carcinogenesis.