  Single crystals of Ruddlesden-Popper nickelates La$_4$Ni$_3$O$_{10}$ were
grown by means of the floating-zone technique at oxygen pressure of 20~bar. Our
results reveal the effects of the annealing process under pressure on the
crystal structure. We present the requirements for crystal growth and show how
a reported ferromagnetic impurity phase can be avoided. The different growth
and post-annealing processes result in two distinct phases $P2_1/a$ and {\it
Bmab} in which the metal-to-metal transitions occur at 152~K and 136~K,
respectively.
