Iterative algorithms, which use diffracted intensities and some a-priori knowledge of an image to solve the phase problem, have been under development for many years. The promised super-resolution images, reconstructed from diffraction information alone, would be of the greatest value for molecular imaging and for the image of nonperiodic structures in materials. Using simulated data it is possible, for example, to reconstruct a complex object from a knowledge of its diffracted intensities with certain known support functions. Some success has recently been achieved reconstructing micrometer-sized non-periodic objects using coherent X-rays by the Feinup method. One favorable support function consists of two holes spanned by the coherence width of the beam, with one or both holes containing an unknown object. Our simulations, which iterate between diffracted intensities and the image, applying the known support (either completely opaque or completely transparent) and intensities in each domain, confirm that image reconstruction is possible for loose supports and noiseless data.