Based on the martingale version of the Skorokhod embedding Heyde and Brown (1970) established a bound on the rate of convergence in the central limit theorem (CLT) for discrete time martingales having finite moments of order 2+2δ with 0<δ⩽1. An extension for all δ>0 was proved in Haeusler (1988). This paper presents a rather quick access based solely on truncation, optional stopping, and prolongation techniques for martingale difference arrays (ξ ni, F ni,1⩽i⩽i(n),n∈ N) to obtain other upper bounds for sup x∈ R |( P( ∑ i1 i(n) ξ ni⩽x)−φ(x)|φ (φbeing the standard normal d.f.) yielding weak sufficient conditions for the asymptotic normality of ∑ i1 i(n) ξ ni . It is shown that our approach also yields two types of martingale central limit theorems with random norming.