Some molecules, particularly aromatics, have high molar extinction coefficients at wavelengths in the damaging ultraviolet radiation region of the spectrum between 200 and 400 nm. Thus, under a UV radiation flux in which these wavelengths are represented, it could be argued that a selection pressure would exist for a UV transparent biochemistry in which they were not represented. This hypothesis is explored using data made available from proteomics, focusing particularly on tryptophan, against which a selection pressure could exist on present-day Earth as a result of its absorbance shoulder at wavelengths greater than 290 nm. The abundance of tryptophan in whole proteomes is lower than expected from the degeneracy of the genetic code. A lower usage of tryptophan is found in the cytochrome c oxidase polypeptide I of UV-exposed organisms compared to nocturnal and subterranean organisms, but not in ATP synthase chain A. Examination of the amino acid composition of photolyase, an enzyme that requires exposure to light to function, shows that the tryptophan abundances exceed those of the total proteome of most organisms and the abundances expected from the degeneracy of the genetic code. This is also true for cytochrome c oxidase, another enzyme that makes extensive use of the electron transfer properties of tryptophan. We suggest that the selection pressure for the use of tryptophan caused, among other factors, by the uses of delocalised pi-electrons that this aromatic provides in active sites and binding motifs outweighs the selection pressure for UV transparency. This trade-off explains the lack of conclusive evidence for a UV transparent selection pressure. We suggest that this trade-off applies to the stacked pi-electrons of DNA. It offers a solution to the long-standing paradox of why the macromolecule responsible for the faithful replication of information has high absorbance in the damaging UV radiation region of the spectrum.