The single-crystal elastic properties of high-spin (Mg0.94Fe0.06)O ferropericlase were measured by Brillouin spectroscopy on a sample compressed to 20 GPa with diamond anvil cells using methanol-ethanol-water as a pressure-transmitting medium. At room pressure, the adiabatic bulk (K0S) and shear (¿0S) moduli are K0S = 163 ¿ 3 GPa and ¿0S = 121 ¿ 2 GPa, in excellent agreement with ultrasonic results from the same bulk sample (Jacobsen et al., 2002). A fit to all our high-pressure Brillouin data using a third-order finite-strain equation of state yields the following pressure derivatives of the adiabatic bulk and shear moduli: K'0S = 3.9 ¿ 0.2 and ¿'0S = 2.1 ¿ 0.1. Within the uncertainties, we find that K0S and K'0S of (Mg0.94Fe0.06)O are unchanged from MgO. However, ¿0S and ¿'0S of (Mg0.94Fe0.06)O are reduced by 8% and 11%, respectively. The aggregate compressional (VP) and shear (VS) wave velocities are reduced by 4% and 6%, respectively, as compared to MgO. The pressure dependence of the single-crystal elastic moduli and aggregate sound velocities is linear within the investigated pressure range. The elastic anisotropy of (Mg0.94Fe0.06)O is about 10% greater than that of MgO at ambient conditions. At the highest pressure obtained here, the elastic anisotropy of (Mg0.94Fe0.06)O is close to zero. On the basis of our measurements and earlier ultrasonic measurements, we find that the pressure derivatives of shear moduli obtained at room pressure for low iron concentrations (<20 mol% FeO) of high-spin ferropericlase are inconsistent with those inferred from the lower mantle PREM model.