The previously presented analytical model of a transversely diode-pumped alkali metal vapour laser (A.I. Parkhomenko, A.M. Shalagin, Quantum Electronics, 2015, Vol. 45, No. 9, pp 797-806) is refined and expanded. Analytical formulas are derived describing the operation of a high-intensity laser at an almost arbitrary buffer gas pressure and taking into account radiation losses in the resonator. Comparison of the results of calculations of the laser energy characteristics by analytical formulas with the results of numerical calculations of other authors shows very good agreement.