It is shown that if a one-dimensional distribution F has finite moment of order 1 + β for some β, 1/2 ≤ β ≤ 1, then the rate of approximation of the n-fold convolution Fⁿ by accompanying laws is O(n^-1/2). Futhermore, if Eξ² = ∞ and 1/2 < β < 1, then the rate of approximation is o(n^-1/2). The question about the true rate of approximation of Fⁿ by infinitely divisible and accompanying laws is discussed.