Fast checkpointing algorithms require distributed access to stable storage. This paper revisits the approach base upon double checkpointing, and compares the blocking algorithm of Zheng, Shi and Kalé, with the non-blocking algorithm of Ni, Meneses and Kalé in terms of both performance and risk. We also extend the model that they have proposed to assess the impact of the overhead associated to non-blocking communications. We then provide a new peer-to-peer checkpointing algorithm, called the triple checkpointing algorithm, that can work at constant memory, and achieves both higher efficiency and better risk handling than the double checkpointing algorithm. We provide performance and risk models for all the evaluated protocols, and compare them through comprehensive simulations.