We arrange the loopwise perturbation theory for the critical viscosity exponent xη, which happens to be very small, as a power series in xη itself and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by xη = 8 15π (1 + 8 3π ) ≃ 0.0685. PACS number(s):64.60Ht