Single crystals of synthetic nickel sulfate monohydrate, alpha-NiSO4 center dot H2O (space-group symmetry C2/ c at ambient conditions), were subject to high-pressure behavior investigations in a diamond-anvil cell up to 10.8 GPa. By means of subtle spectral changes in Raman spectra recorded at 298 K on isothermal compression, two discontinuities were identified at 2.47(1) and 6.5(5) GPa. Both transitions turn out to be apparently second order in character, as deduced from the continuous evolution of unit-cell volumes determined from single-crystal X-ray diffraction. The first structural transition from alpha- to beta-NiSO4 center dot H2O is an obvious ferroelastic C2/c-P (1) over bar transition. It is purely displacive from a structural point of view, accompanied by symmetry changes in the hydrogen-bonding scheme. The second beta- to gamma-NiSO4 center dot H2O transition, further splitting the O2 (hydrogen bridge acceptor) position and violating the P (1) over bar space-group symmetry, is also evident from the splitting of individual bands in the Raman spectra. It can be attributed to symmetry reduction through local violation of local centrosymmetry. Lattice elasticities were obtained by fitting second-order Birch-Murnaghan equations of state to the p-V data points yielding the following zero-pressure bulk moduli values: K-0 = 63.4 +/- 1.0 GPa for alpha-NiSO4 center dot H2O, K-0 = 61.3 +/- 1.9 GPa for beta-NiSO4 center dot H2O, and K-0 = 68.8 +/- 2.5 GPa for gamma-NiSO4 center dot H2O.