  CONTEXT: Spectral-line asymmetries and wavelength shifts are signatures of
hydrodynamics in solar and stellar atmospheres. Theory may precisely predict
idealized lines, but observed spectra are limited by blends, too few suitable
lines, imprecise laboratory wavelengths, and by instrumental imperfections.
  AIMS: Bisectors and shifts are extracted until the 'ultimate' accuracy limits
in highest-quality solar and stellar spectra, to understand limits set by
stellar physics, observational techniques, and limitations in laboratory data.
  METHODS: Spectral atlases of the Sun and bright solar-type stars were
examined for thousands of 'unblended' lines with the most accurate laboratory
wavelengths, yielding bisectors and shifts as averages over groups of similar
lines, thus minimizing effects of photometric noise and of random blends.
  RESULTS: For solar spectra, bisector shapes and shifts were extracted for
previously little-studied species (Fe II, Ti I, Ti II, Cr II, Ca I, C I), using
recently determined very accurate laboratory wavelengths. In Procyon and other
F-type stars, a blueward bend in the bisector near the spectral continuum
reveals line saturation and damping wings in upward-moving photospheric
granules. Accuracy limits set by 'astrophysical' noise, finite instrumental
resolution, superposed telluric absorption, and inaccurate wavelengths,
together limit absolute lineshift studies to approximately 50-100 m/s.
  CONCLUSIONS: Spectroscopy with resolutions R = 300,000 will enable bisector
studies for many stars. Circumventing remaining limits of astrophysical noise
in line-blends and rotationally smeared profiles may ultimately require
spectroscopy across spatially resolved stellar disks.
