  We present the design and realization of two reference cavities for
ultra-stable lasers addressing narrow transitions in mixed-species (In+ / Yb+)
Coulomb crystals. With a simple setup, we achieve a fractional frequency
instability close to the thermal noise limit of a 12 cm long cavity, reaching
4.7 * 10^{-16} at 10 s with a linear drift of 53 mHz/s. We discuss the
individual instability contributions and show that in a setup with a lower
thermal noise floor and vibration sensitivity, an instability of 1 * 10^{-16}
can be reached. To achieve this, we implement a vibration insensitive design
for a 30 cm long cavity mounted horizontally and conduct first tests that show
a sensitivity of 1.8 * 10^{-11} / ms^{-2} to vertical accelerations. This is
about a factor of 20 less than the value observed for the short cavity.
Mechanical tolerances and ways to further reduce the sensitivity are discussed.
