High-speed air intakes with a curved compression ramp (CCR) hold the promise of providing better pressure recovery, higher pressure ratio, and affording shorter lengths compared to conventional intakes. The present work investigates the off-design performance of a model CCR air intake in a wind tunnel at Mach 6. Specifically, the robustness of the intake flow to back-pressure fluctuations and angle-of-attack (AoA) variation is assessed. The intake model, which was designed based on the strong shock design principle, comprises of a CCR and a curved cowl lip that leads into an isolator section with parallel walls. Isolator back-pressure variations were induced by using a sliding plate at the exit; motion of the sliding plate varies isolator exit blockage area and thereby changes the back-pressure. The intake AoA was varied by rotating the support sector in the wind tunnel test section onto which the entire intake model was sting-mounted. Time-resolved pressure and high-speed schlieren measurements were made to understand in detail the flow features internal and external to the intake model, including the dynamics of shock-shock and shock-boundary layer interactions at the cowl and inside the isolator. These experimental results provide new insights into the flow behavior in CCR intakes at off-design conditions.