  We report a high-pressure single crystal study of the topological
superconductor Cu$_x$Bi$_2$Se$_3$. Resistivity measurements under pressure show
superconductivity is depressed smoothly. At the same time the metallic behavior
is gradually lost. The upper critical field data $B_{c2}(T)$ under pressure
collapse onto a universal curve. The absence of Pauli limiting and the
comparison of $B_{c2}(T)$ to a polar state function point to spin-triplet
superconductivity, but an anisotropic spin-singlet state cannot be discarded
completely.
