In order to explore how spectral sparsity and vibronic decoherence pathways can be controlled in a model qubit system with atomic clock transitions, we combined diamond anvil cell techniques with synchrotron-based far infrared spectroscopy and first-principles calculations to reveal the vibrational response of Na9[Ho(W5O18)2]·35H2O under compression. Because the hole in the phonon density of states acts to reduce the overlap between the phonons and f manifold excitations in this system, we postulated that pressure might move the HoO4 rocking, bending, and asymmetric stretching modes that couple with the MJ = ±5, ±2, and ±7 levels out of resonance, reducing their interactions and minimizing decoherence processes, while a potentially beneficial strategy for some molecular qubits, pressure slightly hardens the phonons in Na9[Ho(W5O18)2]·35H2O and systematically fills in the transparency window in the phonon response. The net result is that the vibrational spectrum becomes less sparse and the overlap with the various MJ levels of the Ho3+ ion actually increases. These findings suggest that negative pressure, achieved using chemical means or elongational strain, could further open the transparency window in this rare earth-containing spin qubit system, thus paving the way for the use of device surfaces and interface elongational/compressive strains to better manage decoherence pathways.