We construct supersymmetric D-brane probe solutions in the background of the 2-charge D1-D5 system on M, where M is either K3 or T⁴. We focus on `near-horizon bound states' that preserve supersymmetries of the near-horizon AdS₃ × S³ × M geometry and are static with respect to the global time coordinate. We find a variety of half-BPS solutions that span an AdS₂ subspace in AdS₃, carry worldvolume flux and can wrap an S² within S³ and/or supersymmetric cycles in M.