  Recent study in K-stability suggests that klt singularities whose local
volumes are bounded away from zero should be bounded up to special
degeneration. We show that this is true in dimension three, or when the minimal
log discrepancies of Koll\'ar components are bounded from above. We conjecture
that the minimal log discrepancies of Koll\'ar components are always bounded
from above, and verify it in dimension three when the local volumes are bounded
away from zero. We also answer a question of Han, Liu and Qi on the relation
between log canonical thresholds and local volumes.
