  We exploit an ambiguity somewhat hidden in Noether's theorem to derive
systematically, for relativistic field theories, the stress-energy tensor's
improvement terms that are associated with additional spacetime symmetries
beyond translations. We work out explicitly the cases of Lorentz invariance,
scale invariance, and full conformal invariance. The main idea is to use,
directly in the translation Noether theorem, the fact that these additional
symmetries can be thought of as suitably modulated translations. Compared to
more standard derivations of the improvement terms, ours (1) unifies all
different cases in a single framework, (2) involves no guesswork, (3) yields
the desired algebraic properties (symmetry and/or tracelessness) of the
stress-energy tensor off-shell, and (4) unifies the translation Noether theorem
with those of the additional spacetime symmetries, yielding at the same time
both the improved stress-energy tensor and the additional Noether currents.
