  We study the magnetic field vs temperature ($H$--$T$) and pressure vs
temperature ($P$--$T$) phase diagram of the $T_c \approx 5.5$~K superconducting
phase in Pd$_x$Bi$_2$Te$_3$ ($x \approx 1$) using electrical resistivity versus
temperature measurements at various applied magnetic fields ($H$) and magnetic
susceptibility versus temperature measurements at various applied magnetic
fields ($H$) and pressure ($P$). The $H$--$T$ phase diagram has an initial
upward curvature as observed in some unconventional superconductors. The
critical field extrapolated to $T = 0$~K is $H_c (0) \approx 6$--$10$~kOe. The
$T_c$ is suppressed approximately linearly with pressure at a rate $dT_c/dP
\approx -0.28$~K/GPa.
