The numbers of greenbugs, Schizaphis graminum (Rondani), and bird cherry-oat aphids, Rhopalosiphum padi L., per wheat tiller (stem) were estimated in 189 production winter wheat (Triticum aestivum L.) fields located throughout Oklahoma. Taylor's power law regressions were calculated from these data and used to construct fixed precision sequential sampling schemes for each species. An evaluation data set was constructed from 240 samples taken during three growing seasons from winter wheat fields at four locations in Oklahoma. Wheat cultivar and growth stage were recorded for each field on the day of sampling. Taylor's power law parameters for evaluation fields differed significantly for both species among growing seasons, locations, and plant growth stages. Median precision achieved using the fixed precision sequential sampling schemes for each species departed <20% from expected precision over the range population intensity in the evaluation data. For the 10% of samples with greatest deviation between observed and expected precision, observed precision was 13.8-81.8% greater than that expected precision depending on aphid species and population intensity. For the greenbug, the distribution of the percentage deviation between observed and expected precision was positively skewed, so that the sampling scheme tended to over-predict precision. For the bird cherry-oat aphid, the distribution was more symmetric. Even though precision observed using the sampling schemes frequently varied from expected precision, because of the inevitable consequence of sampling error and environmental variation, the sampling schemes yielded median observed precision levels close to expected precision levels over a broad range of population intensity.