The isothermal equation of state (EoS) of phase E, Mg1.96(7)Fe0.072(5)Si1.04(5)H3.7(8)O6, has been determined using high-pressure single-crystal X-ray diffraction. A third-order Birch Murnaghan EoS fit to pressue-volume data collected from room pressure and temperature to 6.7 GPa reveals that phase E has the lowest bulk modulus, KT = 92.9(7) GPa, and highest pressure derivative of the bulk modulus, K′ = 7.3(2), for any dense hydrous magnesium silicate (DHMS) yet measured. A parameterized third-order Birch-Murnaghan EoS was also fit to the unit-cell parameters which display significant curvature with increasing pressure. This analysis shows that the c-axis (Kc = 89.1(10) GPa) is 6% more compressible than the a-axis (Ka = 94.8(6) GPa), with little of the anisotropy commonly observed in other layered structures. The high K′ is indicative of the similarity to layers of the brucite structure. The introduction of interlayer cation polyhedra to the structure serves to reduce both the anisotropy, by reducing the compressibility perpendicular to the sheets, and the ability to shear, by increasing the coherence between layers.