  There are two redshifts in cosmology: $z_{obs}$, the observed redshift
computed via spectral lines, and the model redshift, $z$, defined by the
effective FLRW scale factor. In general these do not coincide. We place
observational constraints on the allowed distortions of $z$ away from $z_{obs}$
- a possibility we dub redshift remapping. Remapping is degenerate with cosmic
dynamics for either $d_L(z)$ or $H(z)$ observations alone: for example, the
simple remapping $z = \alpha_1 z_{obs} +\alpha_2 z_{obs}^2$ allows a
decelerating Einstein de Sitter universe to fit the observed supernova Hubble
diagram as successfully as $\Lambda$CDM, highlighting that supernova data alone
cannot prove that the universe is accelerating. We show however, that redshift
remapping leads to apparent violations of cosmic distance duality that can be
used to detect its presence even when neither a specific theory of gravity nor
the Copernican Principle are assumed. Combining current data sets favours
acceleration but does not yet rule out redshift remapping as an alternative to
dark energy. Future surveys, however, will provide exquisite constraints on
remapping and any models -- such as backreaction -- that predict it.
