Observed seismic anisotropy gives the most direct information on mantle flow, but it is challenging to image it robustly at global scales. Difficulties in separating crustal from mantle structures in particular can have a strong influence on the imaging. Here we carry out several resolution tests using both real and synthetic data, which show that unconstrained crustal structure can strongly contaminate retrieved radial anisotropy at 100–150 km depth. To efficiently reduce crustal effects, we perform whole‐mantle radially anisotropic tomographic inversions including crustal thickness perturbations as model parameters. Our data set includes short‐period group velocity data, which are sensitive to shallow structure. We perform a series of tests that highlight the advantages of our approach and show that to properly constrain thin oceanic crust in global radially anisotropic inversions, group velocity data with wave periods of at least or shorter are required. Our Moho perturbation model shows thicker crust along subduction zones and beneath the Ontong Java plateau in the southwestern Pacific than in the global crustal model CRUST2.0. These features agree well with other crustal models as well as with refraction survey data and tectonic features in these regions.