In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. We prove that it attains fast rates of convergence under the mean Lp error, p ≥ 1, for a wide class of functions. A key result in our development is a new upper bound for the mean Lp error, p ≥ 1, of a general version of the plug-in estimator. This upper bound may be of independent interest.