Review of recent mineral physics literature shows consistent trends for the influence of Fe and H2O on the bulk modulus (K-0) of wadsleyite and ringwoodite, the major phases of Earth's mantle transition zone (410-660 km). However, there is little consensus on the first pressure derivative, K-0'= (dK/dP)(p=0), which ranges from about 4 to >5 across experimental studies and compositions. Here we demonstrate the importance of K-0' in evaluating the bulk sound velocity of the transition zone in terms of water content and provide new constraints on the effect of H2O on K-0' for wadsleyite and ringwoodite by conducting a comparative compressibility study. In the experiment, multiple crystals of hydrous Fo(90) wadsleyite containing 2.0 and 0.25 wt% H2O were loaded into the same diamond anvil cell, along with hydrous ringwoodite containing 1.4wt% H2O. By measuring their pressure-volume evolution simultaneously up to 32 GPa, we constrain the difference in K0' independent of the pressure scale, finding that H2O has no effect on K-0', whereas the effect of H2O on K-0 is significant. The fitted K-0' values of hydrous wadsleyite (0.25 and 2.0 wt% H2O) and hydrous ringwoodite (1.4 wt % H2O) examined in this study were found to be identical within uncertainty, with K-0 similar to 3.7(2). New secondary-ion mass spectrometry measurements of the H2O content of these and previously investigated wadsleyite samples shows the bulk modulus of wadsleyite is reduced by 7.0(5) GPa/wt% H2O, independent of Fe content for upper mantle compositions. Because K-0' is unaffected by H2O, the reduction of bulk sound velocity in very hydrous regions of transition zone is expected to be on the order of 1.6%, which is potentially detectible in high-resolution, regional seismology studies.