Let Bn denote the open unit ball in Cn. We write V to denote Lebesgue volume measure on Bn normalized so that V(Bn)=1. Fix −1<γ<∞ and let Vγ denote the measure given by dVγ(z)=cγ (1−[mid ]z[mid ]2)γdV(z), for z∈Bn, where cγ=Γ(n+γ+1)/ (n!Γ(γ+1)); then Vγ(Bn)=1. The weighted Bergman space A2,γ(Bn) is the space of all analytic functions in L2(Bn, dVγ). This is a closed linear subspace of L2(Bn, dVγ). Let Pγ denote the orthogonal projection of L2(Bn, dVγ) onto A2,γ(Bn). For a function f∈L∞(Bn) the Toeplitz operator Tf is defined on A2,γ(Bn) by Tfh=Pγ(fh), for h∈A2,γ(Bn). It is clear that Tf is bounded on A2,γ(Bn) with ∥Tf∥[les ]∥f∥∞. In this paper we will consider the question for which f∈L∞(Bn) the operator Tf is compact on A2,γ(Bn). Although a complete answer has been given by the author and D. Zheng (see the next section), the condition for compactness is somewhat unnatural. In this article we will give a more natural description for compactness of Toeplitz operators with sufficiently nice symbols. We will describe compactness in terms of behaviour of the so-called Berezin transform of the symbol, which has been useful in characterizing compactness of Toeplitz operators with positive symbols (see [5, 9]). Before we can define this Berezin transform we need to introduce more notation.