The degree of the generators of the canonical ring of surfaces with p_g=0

It is shown that the canonical ring of a minimal surface of general type with $p_g=0, K^2\geq 2$ is generated by its elements of degree lesser or equal to 5, provided $|2K|$ has no fixed components, and that this bound can be lowered to 4 under the assumption that $|2K|$ is base-point free.