Common-conversion-point (CCP) sorting of P-SV converted-wave data is conventionally done by first sorting data into common asymptotic-conversion-point (CACP) gathers and then computing the involved CCP shifts from analytic approximations. I explore an alternative method where the latter step is replaced by an entirely data-driven approach. Moveout curves of correlated P-P and P-SV reflections in collocated CMP and CACP gathers are first scanned for points of equal slowness. A common-source slowness indicates that the downgoing branches of the P-P and P-SV waves overlap if the conversion occurs at the reflecting interface. The P-SV conversion point is then assumed to be situated underneath the associated P-P wave midpoint. A migration of amplitudes from CACP to CCP gathers is straightforward once the exact CCP position is known. This data-driven approach requires kinematic information only and is exact for laterally homogeneous media with arbitrary strength of anisotropy if horizontal symmetry planes are present at all depths. Both time-offset and τ-p domain implementations are possible, although the latter are preferred.