  We report on some recent developments in algebraic tensor reduction of
one-loop Feynman integrals. For 5-point functions, an efficient tensor
reduction was worked out recently and is now available as numerical C++
package, PJFry, covering tensor ranks until five. It is free of inverse 5-point
Gram determinants, and inverse small 4-point Gram determinants are treated by
expansions in higher-dimensional 3-point functions. By exploiting sums over
signed minors, weighted with scalar products of chords (or, equivalently,
external momenta), extremely efficient expressions for tensor integrals
contracted with external momenta were derived. The evaluation of 7-point
functions is discussed. In the present approach one needs for the reductions a
$(d+2)$-dimensional scalar 5-point function in addition to the usual scalar
basis of 1- to 4-point functions in the generic dimension $d=4-2 \epsilon$.
When exploiting the four-dimensionality of the kinematics, this basis is
sufficient. We indicate how the $(d+2)$-dimensional 5-point function can be
evaluated.
