In this paper, we present a simple probabilistic model for aggregating very large losses into a loss collection. This supposes that “standard” losses come in various possible sizes – small, moderate and large – which, fortunately, seem to occur with decreasing frequency. Standard modeling allows us to infer a probability distribution describing their occurrence. From the historical record, we know that very large losses do occur, albeit very rarely, yet they are not usually included in the available data sets. Such losses should be made part of the distribution for computation purposes. For example, to a bank they may helpful in the computation of economic or regulatory capital, while to an insurance company they may be useful in the computation of premiums of losses due to catastrophic events. We develop a simple modeling procedure that allows us to include very large losses in a loss distribution obtained from moderately sized loss data. We say that a loss is large when it is larger than the value-at-risk (VaR) at a high confidence level. The original and extended distributions will have the same VaR but quite different values of tail VaR (TVaR).