  Shelah considered a certain version of Strong Chang's Conjecture, which we
denote $\text{SCC}^{\text{cof}}$, and proved that it is equivalent to several
statements, including the assertion that Namba forcing is semiproper. We
introduce an apparently weaker version, denoted $\text{SCC}^{\text{split}}$,
and prove an analogous characterization of it. In particular,
$\text{SCC}^{\text{split}}$ is equivalent to the assertion that the the
Friedman-Krueger poset is semiproper. This strengthens and sharpens the results
of Cox, and sheds some light on problems from Usuba and Torres-Perez and Wu.
