  We implement three-dimensional polarization gradient cooling of trapped ions.
Counter-propagating laser beams near $393\,$nm impinge in lin$\,\perp\,$lin
configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in
$^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap
frequency of $2\pi \times 285\,$kHz and $3.3(4)$ at $2\pi\times480\,$kHz, in
the axial and radial directions, respectively. Our measurements demonstrate
that cooling with laser beams detuned to lower frequencies from the resonance
is robust against an elevated phonon occupation number, and thus works well for
an initial ion motion far out of the Lamb-Dicke regime, for up to four ions,
and for a micromotion modulation index $\beta\leq 0.1$. Still, we find that the
spectral impurity of the laser field influences both, cooling rates and cooling
limits. Thus, a Fabry-P\'{e}rot cavity filter is employed for efficiently
suppressing amplified spontaneous emission of the diode laser.
