The dimensionless dissipation coefficient β=εL/U3, whereεis the dissipation rate, U the root-mean-square velocity andLthe characteristic scale of the largest flow structures, isan important characteristic of statistically stationary homogeneous turbulence. In studies of β, the external force is typically isotropic and large scale, and its helicity Hf either zero or not measured. Here, we study the dependence of β on Hf and find that it decreases β by up to 10% for both isotropic forces and shear flows. The numerical finding is supportedby static and dynamical upper bound theory. Both show a relative reduction similar tothe numerical results. That is, the qualitative and quantitative dependence ofβon thehelicity of the force is well captured by upper bound theory. Consequences for the valueof the Kolmogorov constant and theoretical aspects of turbulence control and modellingare discussed in connection with the properties of the external force. In particular, the eddy viscosity in large eddy-simulations of homogeneous turbulence should be decreased by at least 10% in the case of strongly helical forcing.