  High-resolution cross-correlation methods are widely used to discover and to
characterise atomic and molecular species in exoplanet atmospheres. The
characteristic cross-correlation signal is typically represented as a function
of the velocity of the system, and the semi-amplitude of the planet's orbit. We
present Saltire, a fast and simple model that accurately reproduces the shape
of such cross-correlation signals, allowing a direct fit to the data by using a
minimum set of parameters. We show how to use this model on the detection of
atmospheric CO in archival data of the hot Jupiter tau Bootis b, and how
Saltire can be used to estimate the semi-amplitude and rest velocity of high
brightness-ratio binaries. By including the shape of the signal, we demonstrate
that our model allows to robustly derive the signal position up to 10 times
more accurate, compared to conventional methods. Furthermore, we discuss the
impact of correlated noise and demonstrate that Saltire is a robust tool for
estimating systematic uncertainties on the signal position. Saltire opens a new
door to analyse high signal-to-noise data to accurately study atmospheric
dynamics and to measure precise dynamical masses for exoplanets and faint
stellar companions. We show, that the phase-resolved shape of the atmospheric
CCF signal can accurately be reproduced, allowing studies of phase-dependent
signal changes and to disentangle them from noise and data aliases.
