Bounded reduction for Chevalley groups of types E6 and E7

We prove that an element from the Chevalley group of type E-6 or E-7 over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certain proper subsystem subgroup by a bounded number of elementary root elements. The bound is given explicitly. This result is an effective version of the early stabilisation of the corresponding K (1)-functor. We also give a part of the proof of similar hypothesis for E-8.