  The resonant line shape from driving a transition between two states,
$|\rm{a}\rangle$ and $|\rm{b}\rangle$, can be distorted due to a
quantum-mechanical interference effect involving a resonance between two
different states, $|\rm{c}\rangle$ and $|\rm{d}\rangle$, if $|\rm{c}\rangle$
has a decay path to $|\rm{a}\rangle$ and $|\rm{d}\rangle$ has a decay path to
$|\rm{b}\rangle$. This interference can cause a shift of the measured
resonance, despite the fact that the two resonances do not have a common
initial or final state. As an example, we demonstrate that such a shift affects
measurements of the atomic hydrogen 2S$_{1/2}$-to-2P$_{1/2}$ Lamb-shift
transition due to 3S-to-3P transitions if the 3S$_{1/2}$ state has some initial
population.
