Idealized axisymmetric anomalies of potential vorticity (PV) on a midlatitude f-plane and their related response in terms of balanced wind and temperature are investigated with special focus on the static stability in the tropopause region. The PV anomalies are specified such that they can be interpreted as the result of conservative advection in the tropopause region across the gradients of a prescribed background atmosphere with piecewise constant buoyancy frequency squared N². Related cyclones and anticyclones are treated identically except for the sign of the tropopause potential temperature anomaly. Composite profiles of N² are computed, for which the thermal tropopause is used as common reference level and where the number of cyclones in the composite equals the number of anticyclones. One obtains a pronounced peak of N² just above the tropopause and slightly enhanced values below the tropopause in comparison with the background profile. Within the framework of PV inversion various mechanisms are identified. Important contributions to the peak in N² are due to the pronounced cyclone-anticyclone asymmetry in the vertical structure of the tangential wind, and due to the poleward advection of high values of PV from the subtropical lower stratosphere. Qualitatively the key features of the composite profiles are in good agreement with observations above Southern Germany which have recently been compiled.