  We present three "hard" diagrams of the unknot. They require (at least) three
extra crossings before they can be simplified to the trivial unknot diagram via
Reidemeister moves in $\mathbb{S}^2$. Both examples are constructed by applying
previously proposed methods. The proof of their hardness uses significant
computational resources. We also determine that no small "standard" example of
a hard unknot diagram requires more than one extra crossing for Reidemeister
moves in $\mathbb{S}^2$.
