In local earthquake (LE) tomography for P- and S-wave velocities (or Vp/Vs ratios), constraints punishing deviations from a given Vp/Vs ratio are often used. In a synthetic model test we demonstrate that though such constraints inhibit unreasonable Vp/Vs ratio variations, they bias the resulting Vp/Vs ratios. As an alternative approach, structural constraints based on the cross-product of the model gradients can be used to constrain the joint P- and S-wave inversion. We show that the resulting models are as low in artifacts as if a Vp/Vs damping was used, but the resulting Vp/Vs ratios are less biased, which is important for a quantitative interpretation of physical properties and processes in the Earth.