  Precision measurements of the magnetization and ac susceptibility of
Cu$_2$0SeO$_3$ are reported for magnetic fields along different
crystallographic directions, focussing on the border between the conical and
the field-polarized state for a magnetic field along the $\langle 100 \rangle$
axis, complemented by selected specific heat data. Clear signatures of the
emergence of a second skyrmion phase and a tilted conical phase are observed,
as recently identified by means of small-angle neutron scattering. The
low-temperature skyrmion phase displays strongly hysteretic phase boundaries,
but no dissipative effects. In contrast, the tilted conical phase is
accompanied by strong dissipation and higher-harmonic contributions, while the
transition fields are essentially nonhysteretic. The formation of the second
skyrmion phase and tilted conical phase are found to be insensitive to a
vanishing demagnetization factor. A quantitative estimate of the temperature
dependence of the magnetocrystalline anisotropy may be consistently inferred
from the magnetization and the upper critical field and agrees well with a
stabilization of the low-temperature skyrmion phase and tilted conical state by
conventional cubic magnetic anisotropies.
