The material ZrTe3 is a well-known example of an incommensurate periodic lattice distortion (PLD) at low temperatures due to a charge density wave (CDW). Previous studies have found a sharp boundary as a function of pressure between CDW below 5 GPa and bulk superconductivity above this value. We present a study of low-temperature-high-pressure single crystal x-ray diffraction along with ab initio density functional theory calculations. The modulation vector q(CDW) is found to change smoothly with pressure until the PLD is lost. Fermi surface calculations reproduce these changes, but neither these nor the experimental crystal lattice structure show a particular step change at 5 GPa, thus leading to the conclusion that the CDW is lost accidentally by tipping the balance of CDW formation in the Fermi surface nesting that stabilizes it.