We present the results from a global carbon-cycle model which transports 3 isotopes of carbon amongst model reservoirs. Particular emphasis is placed on the dynamics and budget of 14C produced by nuclear weapons testing and augmenting natural cosmogenic production. The evolution of the “bomb 14C” budget, particularly since ca. 1970, has recently been under scrutiny, and our ability to balance it been questioned. These misgivings arose from an inability to simulate simultaneously both the rising atmospheric CO2 and the decline in its 14C/12C ratio. We use the Enting-Lassey carbon-cycle model based on a box-diffusion ocean sub-model to deduce the evolution of the budgets for both anthropogenic carbon and bomb 14C, and show that these can be simultaneously reconciled with tropospheric observation. The bomb 14C inventory in the model ocean is also compatible with a recent re-analysis of GEOSECS data. A key and distinctive feature of our model is the forward integration driven even-handedly by inputs of anthropogenic carbon, both from industrial sources and land use change, and bomb 14C, consistently with documented emission or production patterns.