Polymer models tied together by constraints of looping and confinement have been used to explain many of the observed organizational characteristics of interphase chromosomes. Here we introduce a simple lattice animal representation of interphase chromosomes that combines the features of looping and confinement constraints into a single framework. We show through Monte Carlo simulations that this model qualitatively captures both the leveling off in the spatial distance between genomic markers observed in fluorescent in situ hybridization experiments and the inverse decay in the looping probability as a function of genomic separation observed in chromosome conformation capture experiments. The model also suggests that the collapsed state of chromosomes and their segregation into territories with distinct looping activities might be a natural consequence of confinement. © 2012 American Physical Society.