This paper presents stochastic models and estimation algorithms for speckled images, with an emphasis on synthetic-aperture-radar images, and where the speckle may not be fully developed. We treat speckle from a novel point of view: as a carrier of useful surface information rather than as contaminating noise. The stochastic models for surface scattering are based on a doubly stochastic marked Poisson point process. For each of these surface-scattering statistical models, we present estimation algorithms to determine the average surface reflectivity and scatterer density within a resolution cell, using intensity measurements of speckled images. We show that the maximum-likelihood estimator is optimal in the sense that the variance of the error is the smallest possible using any conceivable estimate having the same bias with the same data.