The problem is to estimate the number of points in and the size of a cluster when the points of the cluster are confounded with points having a smooth density (background or noise). The methods of estimation considered are maximum likelihood, minimumx2of the fit of counts in concentric annuli about the mean, and severalad hocprocedures. They are compared by application to computer simulated clusters where the density of the points in the clusters is assumed to be from a circularly symmetric bivariate distribution. The techniques are suitable for any system composed of individttal points, such as clusters of stars or galaxies, photometry of diffuse objects by digital image recorders, and measurement of energy or momentum of particles in a scattering experiment.