  We show that a set of K-semistable log Fano cone singularities is bounded if
and only if their local volumes are bounded away from zero, and their minimal
log discrepancies of Koll\'ar components are bounded from above. As
corollaries, we confirm the boundedness conjecture for K-semistable log Fano
cone singularities in dimension three, and show that local volumes of
3-dimensional klt singularities only accumulate at zero.
