  We apply point-particle effective field theory (PPEFT) to electronic and
muonic 4He+ ions, and use it to identify linear combinations of spectroscopic
measurements for which the theoretical uncertainties are much smaller than for
any particular energy levels. The error is reduced because these combinations
are independent of all short-range physics effects up to a given order in the
expansion in the small parameters R/a_B and(Z alpha) (where R and a_B are the
ion's nuclear and Bohr radii). In particular, the theory error is not limited
by the precision with which nuclear matrix elements can be computed, or
compromised by the existence of any novel short-range interactions, should
these exist. These combinations of 4He+ measurements therefore provide
particularly precise tests of QED. The restriction to 4He+ arises because our
analysis assumes a spherically symmetric nucleus, but the argument used is more
general and extendable to both nuclei with spin, and to higher orders in R/a_B
and (Z alpha).
