A major obstacle in tomographic inversion is near-surface velocity variations. Such shallow velocity variations need to be known and correctly accounted for to obtain images of deeper structures with high resolution and quality. Bedrock cover in many areas consists of unconsolidated sediments and glacial till. To handle the problems associated with this cover, we present a tomographic method that solves for the 3D velocity structure and receiver static corrections simultaneously. We test the method on first-arrival picks from deep seismic reflection data acquired in the mid- late to 1980s in the Siljan Ring area, central Sweden. To use this data set successfully, one needs to handle a number of problems, including time-varying, near-surface velocities from data recorded in winter and summer, several sources and receivers within each inversion cell, varying thickness of the cover layer in each inversion cell, and complex 3D geology. Simultaneous inversion for static corrections and velocity produces a much better image than standard tomography without statics. The velocity model from the simultaneous inversion is superior to the velocity model produced using refraction statics obtained from standard reflection seismic processing prior to inversion. Best results using the simultaneous inversion are obtained when the initial top velocity layer is set to the near-surface bedrock velocity rather than the velocity of the cover. The resulting static calculations may, in the future, be compared to refraction static corrections in standard reflection seismic processing. The preferred final model shows a good correlation with the mapped geology and the airborne magnetic map.