We consider the decomposition rules for the tensor powers of thesmallest representations of quantum groups of type E. For the caseswhere the rank is not 9, H. Wenzl has found uniform combinatorialbehavior for decomposing certain summands of the tensor powers usingLittelmann paths. From this he describes generators of part of thecentralizer algebras of these summands in terms of R-matrices acting onpath spaces and thus obtains a 2-parameter family of representations ofArtin's braid group that generalizes the BMW-algebras. In currentresearch, with an eye towards extending the results to the affine (rank9) case, we find a submodule of the tensor power whose simpledecomposition follows the same pattern as in the cases considered byWenzl. The summands we define have a finite decomposition, and we showthat the inclusion rules for these summands behave well with respect tothe Littelmann path formalism. We also note that the eigenvalues of theaction of the R-matrices are predicted by Wenzl's formulas and we can safely follow his program for describing the centralizer algebra.