The paper is concerned with the second order asymptotics of distributions of trimmed means \sum_{i=\kn+1}^{n-\mn}\xin$, where $\kn$, $\mn$ are sequences of integers, $0\le \kn <n-\mn \le n$, such that $r_n:=\min(\kn, \mn) \to \infty$, as $\nty$, the $\xin$'s denote the order statistics corresponding to a sample $X_1,\dots,X_n$ of $n$ i.i.d. random variables. In particular, we focus on the case of intermediate trimmed means, when $\max(\kn,\mn)/n\to 0$, as $\nty$. We focus on the case of slightly trimmed means, when max(kn, mn)/n 0 as n ∞. In [11], Berry–Esseen type bounds were obtained for the normal approximation of Tn; under certain regularity conditions, these bounds are of the order $O\bigl(r_n^{-1/2}\bigr)$. In [11], it is also shown that this order cannot be improved if $\textbf{E}X^2_1=\infty$. Moreover, asymptotic Edgeworth type expansions were found in [11] for slightly trimmed means and their Studentized versions. In the present paper, we supplement the results of [11] by Berry–Esseen type b