The frequency of loss of restriction sites may be a limiting factor in the application of RFLPA to phylogenetic investigations of higher taxonomic categories. One purpose of this work is to ascertain whether the applicability of RFLPA can be extended by the use of a class of restriction endonucleases which will here be termed 2n2 cutters, as any base may occupy the middle position of the recognition sequence. Such endonucleases should be less susceptible than, say, 4-base cutters to the redundancy of the genetic code when this position coincides with the third base of a codon. Here the two types of endonucleases are compared by internal statistics summarizing the phylogenetic content of the data and by the concordance of their resulting dendrograms to six known relationships of thirteen acridid and eumustacid grasshoppers. Data were gathered for a mtDNA probe (expected to show redundancy effects) and an rDNA probe (not expected to show such effects). Phenetic and cladistic analyses were performed. There was no evidence that the 2n2-cutting endonucleases produced more accurate dendrograms. In fact, in contrast with expectations and with, as yet, no apparent explanation, trees produced by 4-base cutting endonucleases had greater concordance to present best estimates of grasshopper relationships. The second main purpose of the paper was to extend molecular studies of the phylogeny of the Acrididae. The two main results here were the finding of a close relationship between the Oxyinae and the Catantopinae and the apparent absence of a major endemic Australian radiation in the Acridinae.