  A new approach for the reduction of tensor integrals is described. The
standard decomposition \`{a} la Davydychev is applied. Integrals with higher
indices are then expressed in terms of scalar higher-dimensional integrals with
generic indices. The approach allows to perform contractions with external
momenta in a particularly efficient manner. This is due to the possibility to
perform analytically the resulting sums over the indices of products of signed
minors and scalar products of chords. Advantages of this approach for the
calculation of cross sections are described. We are preparing the numerical
package OLEC (\texttt{O}ne \texttt{L}oop \texttt{E}xternal
\texttt{C}ontractions) with interfaces in Mathematica for algebraic and in C++
for numerical calculations. First numerical results are discussed.
