  We perform a complete analytical reduction of general one-loop Feynman
integrals with five and six external legs for tensors up to rank R=3 and 4,
respectively. An elegant formalism with extensive use of signed minors is
developed for the cancellation of inverse Gram determinants. The 6-point tensor
functions of rank R are expressed in terms of 5-point tensor functions of rank
R-1, and the latter are reduced to scalar four-, three-, and two-point
functions. The resulting compact formulae allow both for a study of analytical
properties and for efficient numerical programming. They are implemented in
Fortran and Mathematica.
