A set of inversion experiments is described that test the ability of global surface wave tomography to retrieve long-wavelength upper mantle velocity structure in the presence of a modest level of rough structure in the presence of a modest level of rough structure. We use upper-mantle model M84A, augmented with randomly-generated lateral structure to smax=20, to calculate coupled-mode synthetic seismograms by means of the subspace projection method. The data kernels for path-integral data observables do not belong to the model space of allowable phase velocity perturbations, suggesting that constraints on model roughness in the inversion should lead to a better agreement with the long-wavelength part of the 'true' model than do the commonly-used constraints on model size. Coherence C between the inverted and the input model is enhanced by using roughness constraints. Estimation of perturbation size is more stable using roughness constraints, but is subject to a positive bias, especially for periods T>200 s. We can achieve, with a data set of 672 R1 and R2 phase delays, C≥0.9 only for s≤6, suggesting 'leakage' bias caused by the breakdown of the pure-path assumption. ¿ American Geophysical Union 1989