  We extend the Doering-Constantin approach to upper bounds on energy
dissipation in turbulent flows by introducing a balance parameter into the
variational principle. This parameter governs the relative weight of different
contributions to the dissipation rate. Its optimization leads to improved
bounds without entailing additional technical difficulties. For plane Couette
flow, the high-Re-bounds obtainable with one-dimensional background flows are
methodically lowered by a factor of 27/32.
