  Cuprate superconductors have a universal tendency to form charge density-wave
(CDW) order which competes with superconductivity and is strongest at a doping
$p \simeq 0.12$. Here we show that in the archetypal cuprate
YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO) pressure suppresses charge order, but does not
affect the pseudogap phase. This is based on transport measurements under
pressure, which reveal that the onset of the pseudogap at $T^*$ is independent
of pressure, while the negative Hall effect, a clear signature of CDW order in
YBCO, is suppressed by pressure. We also find that pressure and magnetic field
shift the superconducting transition temperature $T_{\rm c}$ of YBCO in the
same way as a function of doping - but in opposite directions - and most
effectively at $p \simeq 0.12$. This shows that the competition between
superconductivity and CDW order can be tuned in two ways, either by suppressing
superconductivity with field or suppressing CDW order by pressure. Based on
existing high-pressure data and our own work, we observe that when CDW order is
fully suppressed at high pressure, the so-called "1/8 anomaly" in the
superconducting dome vanishes, revealing a smooth $T_{\rm c}$ dome which now
peaks at $p \simeq 0.13$. We propose that this $T_{\rm c}$ dome is shaped by
the competing effects of the pseudogap phase below its critical point
$p^{\star} \sim 0.19$ and spin order at low doping.
