  This paper enriches the list of properties of the congruence sequences
starting from the universal relation and successively performing the operations
of lower $t$ and lower $k$. Three classes of completely regular semigroups,
namely semigroups for which $\ker{\sigma}$ is a cryptogroup, semigroups for
which $\ker{\nu}$ is a cryptogroup and semigroups for which $\kappa$ is over
rectangular bands, are studied. $((\omega_t)_k)_t$, $((\mathcal{D}_t)_k)_t$ and
$((\omega_k)_t)_k$ are found to be the least congruences on $S$ such that the
quotient semigroups are semigroups for which $\ker{\sigma}$ is a cryptogroup,
$\ker{\nu}$ is a cryptogroup and $\kappa$ is over rectangular bands,
respectively. The results obtained present a response to three problems in
Petrich and Reilly's textbook \textquoteleft\textquoteleft Completely Regular
Semigroups\textquoteright\textquoteright.
