The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, e, that maintains the balanced state. We find that a surprisingly low e suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes. P URIFYING selection maintains well-adapted genotypes in the face of deleterious mutations ). Yet in asexual populations, random genetic drift in the most-fit class of individuals will occasionally lead to its irreversible extinction, a process known as Muller's ratchet (Muller 1964;Felsenstein 1974). The repetitive action of the ratchet leads to the accumulation of deleterious mutations, despite the action of purifying selection. This ratchet effect has been extensively analyzed (Gessler 1995;Charlesworth and Charlesworth 1997; Gordo and Charlesworth 2000a,b; and has been observed in experiments (Chao 1990;Duarte et al. 1992;Andersson and Hughes 1996;Zeyl et al. 2001) and in nature (Rice 1994;Lynch 1996;Howe and Denver 2008). In small populations when deleterious mutation rates are high or selection pressures are weak, the ratchet can proceed quickly, causing rapid degradation of asexual genomes Lynch et al. , 1995. Hence Muller's ratchet has been described as a central problem for the maintenance of asexual populations such as mitochondria (Loewe 2006). Avoiding this mutational catastrophe is thought to be a major benefit of sex and recombination (see Barton and Charlesworth 1998 and De Visser and Elena 2007 for reviews).However, new studies indicate that natural and laboratory asexual populations do not always melt down as predicted. For example, recently showed that even very small laboratory populations of phage with high mutation rates tend toward fitness plateaus. In addition, a recent comparison of human, chimpanzee, and rhesus Y chromosomes demonstrated that after an initial period of degradation following the halt of recombination, gene loss in the human Y chromosome effectively stopped (Hughes et al. 2...