A combined model for current profile control and MHD stabilityanalysis has been used to identify stable operating modes near theideal stability limit (βN ≃ 3) in the AlcatorC-Mod tokamak. These discharges are characterized by relatively highfractions of bootstrap current (fBS = 0.70) andnon-monotonic profiles of the safety factor with qmin > 2. Inthe absence of a conducting shell, stability was determined bythe onset of the low (n = 1) external kink mode. In these studies,current profile control in the plasma periphery (r/a ≳ 0.5)was provided by 2.5-3.0 MW of LHCDpower. Internal and edge transport barriers were introduced into the model calculations in the form of density transitions. Excellent waveaccessibility and absorption were still found in the presence of anH-mode-like edge density barrier. However, the presence of thesebarriers resulted in about a 10% decrease in the stability limit, fromβN ≃ 3 to βN ≃ 2.7.