This paper presents an improved rational method for predicting the punching strength of conventional reinforced concrete slab-column specimens extending to the nominal line of contraflexure in a flat slab structure. The proposed method of analysis is for square and circular, isotropically reinforced, conventional slab-column specimens, concentrically loaded using square or circular columns. The method is based on an earlier two-phase approach, in which the punching strength was predicted as the lesser of the flexural punching strength and the shear punching strength. The earlier approach had previously been shown to be more reliable than other methods, including the major building code methods, and the proposed method represents a further significant improvement. The improvement in the proposed method is due to the incorporation of slab depth factors for both the flexural and shear modes of punching failure and refinements to the effects of concrete strength, reinforcement percentage and reinforcement yield strength, for the shear mode of punching failure. Comprehensive test data is presented for 217 tests on conventional slab-column specimens reported in the literature in the sixty year period 1956 - 2016. Analysis of these results by the proposed method resulted in significantly improved correlation over that of the authors’ previous two-phase approach. The method is also shown to be significantly more accurate and consistent than the current Eurocode 2 (2004) method, the ACI 318-14 (2014) method and the fib Model Code (2010) method for predicting the punching strength of conventional reinforced concrete slab-column specimens.