This paper analyzes the problem of deconvolution, especially for signals with peak-like structures. We present and analyze a so-called 'practical approach', which mainly consists of a wavelet shrinkage. It is shown that this practical approach is indeed a regularization procedure, and furthermore, it leads to a convergence rate that is superior to classical linear regularization theory. Our results are based on modeling signals and operators in Besov spaces, especially exploiting the fact that peaks have higher regularity in Besov spaces than in Sobolev spaces.