\indent we consider a model of asexually reproducing individuals. the birth and death rates of the individuals are affected by a fitness parameter. the rate of mutations that cause the fitnesses to change is proportional to the population size, $n$. the mutations may be either beneficial or deleterious. in a paper by yu, etheridge and cuthbertson (2009) it was shown that the average rate at which the mean fitness increases in this model is bounded below by $\text{log}^{1-\delta}n$ for any $\delta > 0$. we achieve an upper bound on the average rate at which the mean fitness increases of $o(\text{log}\hspace{1pt}n/\text{log log} \hspace{1pt}n)$.