  We consider two nonparametric procedures for estimating a concave
distribution function based on data corrupted with additive noise generated by
a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML)
estimator and least squares (LS) estimator, we state qualitative properties,
prove consistency and propose a computational algorithm. For the LS estimator
and its derivative, we also derive the pointwise asymptotic distribution.
Moreover, the rate $n^{-2/5}$ achieved by the LS estimator is shown to be
minimax for estimating the distribution function at a fixed point.
