Most multiple removal algorithms focus on multiples of primary P-wave reflections; removal of multiples of converted reflections have not received comparable attention, so explicit consideration is overdue. A target-oriented algorithm predicts converted wave multiples by coupling apparent slownesses, and then subtracts them from elastic common-source data in a data-adaptive window. Prediction is based on matching apparent slownesses in common-source and common-receiver gathers at all source and receiver locations along the propagation path. Predictions use only offset and traveltime, of the primary pure and converted waves that produce the multiples, picked from common-source gathers, and the slownesses calculated from them. Higher-order multiples can be predicted by repeating this process to match slownesses at a sequence of alternating source and receiver locations in turn. Primary reflections (e.g., SS, SP, and PS) that are considered to be noise, can also be subtracted. The predictions are data-driven and require no velocities, angles, reflector orientations or free-surface topography. Any single component (usually vertical) may be used to identify and pick the traveltimes. The resulting predictions are also valid for all other components. The subtraction involves flattening the predicted time trajectory of the multiple, followed by trace averaging to estimate the local wavelet at each location in a moving trace and time window that contains the wavelet of the multiple. The subtraction is data-adaptive, and implicitly involves amplitude and phase information, so separate or prior estimation of the source time or directivity functions is not required. Two synthetic examples showed that the slowness-based algorithm is successful in predicting and reducing converted wave multiples in an elastic medium. Migrated P-wave subsurface images are generated before and after multiple removal to evaluate the performance. Polarity correction of the horizontal component (either before or after subtraction) ensures coherent stacking.