In this paper, we study the theory of complements, introduced by Shokurov, for Calabi–Yau type varieties with the coefficient set [0, 1]. We show that there exists a finite set of positive integers $\mathcal{N}$, such that if a threefold pair $(X/Z\ni z,B)$ has an $\mathbb{R}$-complement which is klt over a neighborhood of z, then it has an n-complement for some $n\in \mathcal{N}$. We also show the boundedness of complements for $\mathbb{R}$-complementary surface pairs.