High background may result from the presence of hemoglobin in your sample. Hemoglobin (Hb) has a significant absorption at 340 nm and can raise the background signal. One way to circumvent this is to dilute the samples. If you believe hemoglobin background still may be an issue, you may be able to remove the protein by treatment with 0.5 mM Zinc Sulfate as reported in the following reference: C.G. Hover et al. (2000)