The stability limit of a tip-stalling axial compressor is sensitive to the magnitude of the near-casing blockage. In transonic compressors, the presence of the passage shock could be a major cause for the blockage. Identification and elimination of this blockage could be a key to improving the stability limit of the compressor. In this article, using numerical simulation, the near-casing blockage within the transonic rotor, NASA Rotor 37, is quantified using a blockage parameter. For a smooth casing, the blockage at conditions near stall is maximum at about 20% of the tip axial chord downstream of the tip leading edge. This maximum blockage location is found to be consistent with the location of the passage shock–tip leakage vortex interaction. A datum single casing groove design that minimizes the peak blockage is found through an optimization approach. The stall margin improvement of the datum casing groove is about 0.6% with a negligible efficiency penalty. Furthermore, the location of the casing groove is varied upstream and downstream of the datum location. It is shown that the stability limit of the compressor is best improved when the blockage is reduced upstream of the peak blockage location. This article also discusses the prospects of a multigroove casing configuration.