  The effect of hydrostatic pressure (P) on charge density waves (CDW) in
YBa2Cu3Oy has recently been controversial. Using NMR, we find that both the
short-range CDW in the normal state and the long-range CDW in high fields are,
at most, slightly weakened at P=1.9 GPa. This result is in contradiction with
x-ray scattering results finding complete suppression of the CDW at ~1 GPa and
we discuss possible explanations of this discrepancy. Quantitative analysis,
however, shows that the NMR data is not inconsistent with a disappearance of
the CDW on a larger pressure scale, typically ~10-20 GPa. We also propose a
simple model reconciling transport data with such a hypothesis, provided the
pressure-induced change in doping is taken into account. We conclude that it is
therefore possible that most of the spectacular increase in Tc upon increasing
pressure up to ~15~GPa arises from a concomitant decrease of CDW strength.
