We consider the problem of estimating a continuous bounded probability density function when independent data (X_{1}, \ldots, X_{n}) from the density are partially contaminated by measurement error. In particular, the observations (Y_{1}, \ldots, Y_{n}) are such that (P\left(Y_{i}=X_{i}\right)=p) and (P\left(Y_{i}=X_{i}+\varepsilon_{i}\right)=1-p), where the errors (\varepsilon_{i}) are independent (of each other and of the (X_{j}) ) and identically distributed from a known distribution. When (p=0) it is well known that deconvolution via kernel density estimators suffers from notoriously slow rates of convergence. For normally distributed (\varepsilon_{j}) the best possible rates are of logarithmic order pointwise and in mean square error. In this paper we demonstrate that for merely partially ((0<p<1)) contaminated observations (where of course it is unknown which observations are contaminated and which are not) under mild conditions almost sure rates of order (O\left(\left(\left(\log h^{-1}\right) / h h\right)^{1 \cdot 2}\right)) with (h=h(n)=) const ((\log n / n)^{1.5}) are achieved for convergence in (L_{\text {, }})-norm. This is equal to the optimal rate available in ordinary density estimation from direct uncontaminated observations ((p=1)). A corresponding result is obtained for the mean integrated squared error. " 1995 Academic Press. Inc.