Anisotropic seismic full-waveform inversion (FWI) is a challenging task. In the case of 2D vertically transversely isotropic (VTI) media, there are five independent model parameters. This relatively large number of different parameter types imposes significant trade-off issues and makes the inversion parameterization a challenging task. The problem is less severe in a crosshole configuration, in which a wider angular coverage of the region of interest is available. There exist many suggestions for suitable inversion parameterizations. We have determined that, for a crosshole configuration, a relatively simple velocity-based parameterization provides a good FWI reconstruction of the subsurface. Furthermore, considerable improvements of the tomographic images can be achieved by supplying structural similarity constraints using cross gradients to the inversion problem. With two synthetic data sets, we determine that a structurally constrained VTI FWI workflow produces sharper subsurface images without adversely affecting the parameter trade-off issue. With a second synthetic experiment, we find that structurally constrained VTI FWI is robust to major differences in anomaly locations for different parameter types. We successfully applied the methodology to a crosshole data set acquired to image a downscaled version of a high-level radioactive waste repository. The resulting tomograms allowed a narrow highly fractured zone to be imaged.