This paper investigates the minimum risk threshold for wavelet coefficients with additive, homoscedastic, Gaussian noise, and for a soft-thresholding scheme. We start from N samples from a signal on a continuous time axis. For piecewise smooth signals, and for N → ∞, this threshold behaves as C √(2 logN) σ, where σ is the noise standard deviation. The paper contains an original proof for this asymptotic behavior as well as an intuitive explanation. This behavior is necessary to prove the asymptotic optimality of a generalized cross validation procedure in estimating the minimum risk threshold.