Theoretical arguments are presented which suggest that each advance of Muller's 
ratchet in a haploid asexual population causes the fixation of a deleterious 
mutation at a single locus. A similar process operates in a diploid, fully 
asexual population under a wide range of parameter values, with respect to 
fixation within one of the two haploid genomes. Fixations of deleterious 
mutations in asexual species can thus be greatly accelerated in comparison with 
a freely recombining genome, if the ratchet is operating. In a diploid with 
segregation of a single chromosome, but no crossing over within the chromosome, 
the advance of the ratchet can be decoupled from fixation if mutations are 
sufficiently close to recessivity. A new analytical approximation for the rate 
of advance of the ratchet is proposed. Simulation results are presented that 
validate the assertions about fixation. The simulations show that none of the 
analytical approximations for the rate of advance of the ratchet are 
satisfactory when population size is large. The relevance of these results for 
evolutionary processes such as Y chromosome degeneration is discussed.