  We present updated predictions for lifetimes of doubly charmed baryons,
within the heavy quark expansion, including available NLO $\alpha_s$
contributions and newly-computed terms in the $1/m_c$ series. Our improved
results confirm the expected hierarchy $$\tau(\Xi_{cc}^{+}) <
\tau(\Omega_{cc}^{+}) < \tau(\Xi_{cc}^{++}) \,, $$ while the predicted lifetime
$\tau(\Xi_{cc}^{++}) = 0.32 \pm 0.5 ^{+0.8}_{-0.7} \,\textrm{ps} $ is
consistent with the recent LHCb determination. We provide predictions for the
lifetime ratios of the $\Xi_{cc}^{+}$ and $\Omega_{cc}^+$ baryons relative to
the $\Xi_{cc}^{++}$ baryon, namely
$\tau(\Xi_{cc}^{+})/\tau(\Xi_{cc}^{++})=0.22\pm 0.05\pm 0.04$ and
$\tau(\Omega_{cc}^{+})/\tau(\Xi_{cc}^{++})=0.52\pm 0.13^{+0.03}_{-0.02}$.
