Observational evidence indicates that upper-tropospheric and lower-stratospheric anticyclones occur in mesoscale convective systems, possibly resulting from the vertical redistribution of mass. The authors examine the gradient adjustment process that occurs when mass from the lower troposphere is impulsively injected between isentropic levels in the vicinity of the tropopause. Formulating the quasi-static primitive equations for inviscid, adiabatic, axisymmetric flow on an f plane using entropy and potential radius coordinates allows us to compute the final state in gradient balance by solving a single nonlinear elliptic problem. Solutions of this elliptic problem illustrate the development of an anticyclonic lens at the level of mass injection, with accompanying cold and warm temperature anomalies above and below, respectively. For a given amount of injected mass, a lower-stratospheric injection results in a stronger anticyclone than does an upper-tropospheric injection. Mass injections at low latitudes result in anticyclonic lens structures that are of larger horizontal extent and smaller vertical extent. The entrainment of stratospheric air into the mesoscale convective anvil is also shown to have an effect on the structure of the anticyclone. The theoretical results presented here are in substantial agreement with recent observations of the structure of upper-level anticyclones produced by mesoscale convective systems.