  Total charm-pair cross sections in $pp$ collisions are interesting because
they can be calculated to NNLO in QCD without any reference to fragmentation
effects. On the other hand, the fiducial differential charm cross sections from
which the total cross sections must be extrapolated are currently known to
NLO+NLL at most (e.g. FONLL), and must be treated for known effects of
nonuniversal charm fragmentation. A new procedure using the FONLL framework as
input for an empirical parametrization of the data in both shape and
normalization, with all its parameters actually fitted to data, is used to
derive so-called data-driven FONLL (ddFONLL) parametrizations which can be used
to extrapolate the differential cross sections to total cross sections with
minimal bias. This includes an empirical treatment of all known non-universal
charm fragmentation effects, in particular for the baryon-to-meson ratio as a
function of transverse momentum. The total charm-pair cross sections obtained
in this way, which supersede all previous ones obtained using the assumption of
charm-fragmentation universality, are consistent with NNLO predictions, and
allow first studies of their sensitivity e.g. to the charm-quark mass and/or
the NNLO gluon PDF at very low transverse momentum fractions $x$.
