Communication-induced checkpointing (CIC) protocols can be used to prevent the domino effect. The fully-informed (FI) protocol proposed in the literature is known as the best CIC protocol so far. In this paper, we investigate some properties of such a protocol. First, we discover that an enhancement adopted by the FI protocol rarely takes effect in practice. In particular, we prove that such an enhancement is invalid over a tree communication network. Moreover, the size of the control information that the FI protocol piggybacks on application messages can be further reduced on such a type of network. Next, we show how to apply the FI protocol to another improved indexing strategy introduced in the literature. The management of a boolean array in its control information carried on a message must be modified. Finally, we present a simulation study to analyze the properties of the FI protocol.