  The dimensionless dissipation coefficient $\beta=\varepsilon L/U^3$ is an
important characteristic of statistically stationary homogeneous turbulence. In
studies of $\beta$, the external force is typically isotropic and large-scale,
and its helicity $H_f$ either zero or not measured. Here, we study the
dependence of $\beta$ on $H_f$ and find that it decreases $\beta$ by up to
10$\%$ for both isotropic forces and shear flows. The numerical finding is
supported by static and dynamical upper bound theory. Both show a relative
reduction similar to the numerical results. That is, the qualitative and
quantitative dependence of $\beta$ on the helicity of the force is well
captured by upper bound theory. Consequences for the value of the Kolmogorov
constant and theoretical aspects of turbulence control and modelling are
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 about 10$\%$ in case of strongly helical
forcing.
