Summary: The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the \(L^\infty\)-norm of the gain term can be bounded in terms of the \(L^1\)- and \(L^\infty\)-norm of the density function \(f\). In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the \(L^\infty\)-norm of the density function and the loss term of the Boltzmann collision operator.