It is well known that when s, the selection coefficient against a deleterious mutation, is below approximately 1/4Ne, where Ne is the effective population size, the expected frequency of this mutation is approximately 0.5, if forward and backward mutation rates are similar. Thus, if the genome size, G, in nucleotides substantially exceeds the Ne of the whole species, there is a dangerous range of selection coefficients, 1/G < s < 1/4Ne. Mutations with s within this range are neutral enough to accumulate almost freely, but are still deleterious enough to make an impact at the level of the whole genome. In many vertebrates Ne approximately 10(4), while G approximately 10(9), so that the dangerous range includes more than four orders of magnitude. If substitutions at 10% of all nucleotide sites have selection coefficients within this range with the mean 10(-6), an average individual carries approximately 100 lethal equivalents. Some data suggest that a substantial fraction of nucleotides typical to a species may, indeed, be suboptimal. When selection acts on different mutations independently, this implies too high a mutation load. This paradox cannot be resolved by invoking beneficial mutations or environmental fluctuations. Several possible resolutions are considered, including soft selection and synergistic epistasis among very slightly deleterious mutations.