Lewark has shown that sl(3)-link homology can be computed efficiently for a reasonable class of links. Furthermore, he was able to show from his calculations that sl(3)-s-invariants behave differently to their counterparts coming from Khovanov homology or link Floer homology. In this talk, we refine the techniques for computing the sl(3)-s-invariant to avoid ambiguities, and also discuss the dependence on the characteristic of the ground field. For links, the Beliakova and Wehrli s-invariant carries over to sl(3)-link homology, but, again, cannot be simply read off a spectral sequence calculation in general. We describe a method to exactly compute this invariant without increasing the complexity.