  The transition metal dichalcogenide PdTe$_2$ has attractive features based on
its classification as a type-II Dirac semimetal and the occurrence of type-I
superconductivity, providing a platform for discussion of a topological
superconductor. Our recent work revealed that type-I superconductivity persists
up to pressures of $\sim2.5$ GPa and the superconducting transition temperature
$T_{\rm c}$ reaches a maximum at around 1 GPa, which is inconsistent with the
theoretical prediction. To understand its non-monotonic variation and
investigate superconductivity at higher pressures, we performed structural
analysis by x-ray diffraction at room temperature below 8 GPa and electrical
resistivity measurements at low temperatures from 1 to 8 GPa. With regard to
the superconductivity beyond 1 GPa, the monotonic decrease in $T_{\rm c}$ is
reproduced without any noticeable anomalies; $T_{\rm c}$ changes from 1.8 K at
1 GPa to 0.82 K at 5.5 GPa with $dT_{\rm c}/dP\sim-0.22$ K/GPa. The crystal
structure with spacegroup $P$\={3}$m$1 is stable in the pressure range we
examined. On the other hand, the normalized pressure-strain analysis (finite
strain analysis) indicates that the compressibility changes around 1 GPa,
suggesting that a Lifshitz transition occurs. We here discuss the effect of
pressure on the superconducting and structural properties based on the
comparison of these experimental results.
