We show that there exists a positive real number
δ
>
0
\delta >0
such that for any normal quasi-projective
Q
\mathbb {Q}
-Gorenstein
3
3
-fold
X
X
, if
X
X
has worse than canonical singularities, that is, the minimal log discrepancy of
X
X
is less than
1
1
, then the minimal log discrepancy of
X
X
is not greater than
1
−
δ
1-\delta
. As applications, we show that the set of all noncanonical klt Calabi–Yau
3
3
-folds are bounded modulo flops, and the global indices of all klt Calabi–Yau
3
3
-folds are bounded from above.