The paper discusses some observeti characteristics which have not been taken into account in previous theoretical studies. For instance, a well-mixed convective boundary layer is a common feature of the synoptic situation when polar lows are observed. However, in the polar lows themselves, the convection seems to reach much higher levels. Also, many polar lows have a characteristic central domain with especially strong winds and large vorticity.A simple linear CISK model is used to estimate the intensification caused by the convection. The model is based on constraints imposed by the assumption of a well-mixed convective layer. Elements of the cloud physics are used to explain observed characteristics of clouds and precipitation. Finally, it is shown that additional growth rate may be expected if CISK is present in an environment of large relative vorticity. An observed case is studied in the light of the general ideas set forth in this paper.