Crosswell traveltime tomography is a common technique in the oil industry for determining the velocity function in the plane between two boreholes. However, the method suffers from the well-known problem that the lateral resolution is far less than the vertical resolution because of the unfavorable illumination conditions for survey geometries comprising vertical wells. Consequently, it is very difficult to image sudden lateral changes in the velocity function accurately using this technique. We propose a method for determining such changes, which severely constrains the solution space by inverting for the position of a lateral velocity contrast only. The velocity model on each side of the contrast is derived from the well logs. The potential of the method is first demonstrated in two synthetic examples in which its properties are compared with those of an unconstrained 2-D tomographic inversion. As expected, the constrained method has much better convergence properties than the unconstrained one in these examples. We also compare the two methods in a real setting, in which a sudden lateral velocity change, associated with a geological transition, is expected. It turns out that a lateral contrast can be imaged with both methods in this real data example. However, the image obtained with the new method better explains the observed facts.