  Extensions of the Standard Model which involve a new scale, $\Lambda$, may,
for energies sufficiently small compared to this new scale, be expressed in
terms of operators with energy dimension greater than four. The coefficients of
just four SU(2)$\times$U(1)-gauge-invariant energy-dimension-six operators are
sufficient to parameterize the contributions of new physics in the electroweak
bosonic sector to electroweak precision measurements. In this letter we update
constraints on the coefficients of these four operators due to recent precision
measurements of electroweak observables. We further demonstrate how such
constraints may be improved by experiments at TRISTAN, LEP2 and at a future
linear $e^+e^-$ collider. The relationship of these operators to the oblique
parameters $S$, $T$ and $U$ is examined. Two of the operators contribute to a
non-standard running of the electroweak charge form-factors
$\overline{\alpha}(q^2)$, $\overline{s}^2(q^2)$, $\overline{g}_Z^2(q^2)$ and
$\overline{g}_W^2(q^2)$; in the special case where the coefficients of these
two vanish the operator analysis reduces to an analysis in terms of $S$, $T$
and $U$ with $U = 0$.
