Regularity of Koszul modules

Let $K$ be a field and let $S=K[X_1,\dots ,X_n]$. Let $I$ be a graded ideal in $S$ and let $M$ be a finitely generated graded $S$-module. We give upper bounds on the regularity of Koszul homology modules $H_i(I,M)$ for several classes of $I$ and $M$.