Dense acquisition are more and more available in exploration and earthquake seismology. Tomographic approaches can now consider not only travel times but also the wavefront itself across the seismic network (Zhang and Thurber, 2003; Yuan et al., 2016). For dense controlled-source seismic experiments, double differences of travel times between receivers in a common-shot gather (resp between sources in a common-receiver gather) are estimated, namely the horizontal component of the slowness vector at source and receiver positions designed as slopes. These slopes associated with the two-way traveltimes are interpreted as a reflection/diffraction from a small reflector segment or diffractor are used in tomographic inversion (Lambaré, 2008; Tavakoli F. et al., 2017). Picking of locally-coherent events leads to dense volumetric dataset and hence higher-resolution tomographic results (Guillaume et al., 2008). The reflection setting introduces implicitly another class of unknowns which are scatterer positions. Resulting inverse problem is awkward due to the intrinsic coupling between velocities and scatterer positions. The first choice alternates positions and wavespeeds. The second performs the joint estimation of the two parameter classes. The third one relies on the projection of the scatterer positions subspace onto the wavespeed subspace leading to a reduced-space inversion. This reduced-space formulation can be implemented in the slope tomography using adjoint-state method. Two focusing equations, which depend on two observables among the three available ones (two-way traveltime and one slope in 2D), gives exact solutions of positions which are injected as constraints in the slope tomography (Chauris et al., 2002). These constraints explicitly enforce the positions in the velocity estimation problem, which reduces now to a mono-variate inverse problem by minimization of single-slope residuals, not yet used. 2D synthetic (see figure) and real data case studies show faster convergence toward more accurate minimizer achieved by this variable projection method compared to the alternated and joint strategies. This method, which can be extended to 3D configurations, draws also interesting perspective for the joint hypocenter-velocity inversion problem in earthquake seismology.