The literature on communication-induced checkpointing presents a family of protocols that use logical clocks to control whether forced checkpoints must be taken. Efficiency of these protocols is measured by how many forced checkpoints are needed to ensure no checkpoint will be useless to the application; the fewer forced checkpoints the better. For many years, HMNR, also called Fully Informed (FI), was the most complex and efficient protocol of this family. The Lazy-FI protocol applies a lazy strategy that defers the increase of logical clocks, resulting in a protocol with better efficiency for distributed systems where processes can take basic checkpoints at different rates. Recently, the Fully Informed aNd Efficient (FINE) protocol was proposed using the same control structures as FI, but with a stronger and, presumably better, checkpoint-inducing condition. FINE and its lazy version, called Lazy-FINE, would now be the most efficient checkpointing protocols based on logical clocks. This paper reviews this family of protocols, proves a theorem on a condition that must be enforced by all stronger versions of FI, and proves that both FINE and Lazy-FINE do not guarantee the absence of useless checkpoints. As a consequence, FI and Lazy-FI can be rolled back to the position of most efficient protocols of this family of index-based checkpointing protocols.