A polymer chain in a poor solvent collapses to a spherical globule. If this globule is subsequently deformed, either by stretching it or if it has some non-zero net electric charge, it will become unstable to sinusoidal perturbations leading to novel final states. When such globules are imaged by direct methods such as atomic force microscopy the substrate on which they adsorb can affect the final morphological state. We therefore investigate strongly adsorbed polymers in poor solvents. We demonstrate that the real-space, Self-Consistent Field method is an ideal numerical tool in predicting equilibrium morphologies. New structures are predicted, which support previous explicit free energy calculations. (c) 2007 Wiley Periodicals, Inc.