The equation of state of synthetic deuterated burtite, CaSn(OD)6, has been determined to 7.25 GPa at 298 K by synchrotron X-ray powder diffraction. Fitting to a third-order Birch-Murnaghan equation of state gives K0 = 44.7(9) GPa and K0′ = 5.3(4). A second-order fit gives K0 = 47.4(4) GPa. Within experimental error the two fits are indistinguishable over the pressure range studied. The decrease in the a parameter with pressure is smooth and no phase transitions were observed. Burtite is much more compressible (by a factor of three or four) than CaSnO3 and CdSnO3 perovskites, indicating that the absence of a cavity cation has a major effect upon the compressibility of the octahedral framework. Burtite is also markedly more compressible than the closely-related mineral stottite FeGe(OH)6 (K0 = 78 GPa). Their different compressibilities correlate with the relative compressibilities of stannate and germanate perovskites. Although different octahedral compressions are likely to be the primary reason for the different compressibilities of burtite and stottite, we also consider the possible secondary role of hydrogen-bonding topology in affecting the compressibilities of protonated octahedral frameworks. Burtite and stottite have different hydrogen-bonding topologies due to their different octahedral-tilt system. Burtite, space group Pn3̅ and tilt system a+a+a+, has a hydrogen-bonded network of linked four-membered rings of O-H...O linkages, whereas stottite, space group P42/n and tilt system a+a+c−, has <100> O-H...O crankshafts and isolated four-membered rings. These different hydrogen-bonded configurations lead to different bracing of the empty cavity sites by the O-H...O linkages and very different hydrogen-bonding connectivities in these two minerals that may also enhance the difference between their compressibilities.