Experimental and theoretical aspects of carbon-13 line shapes in static solids are described for on-resonance spin decoupling conditions. A relatively simple theoretical approach is provided for describing line shapes in static solids based on an operator representation of static second-order perturbation theory and theoretical line shapes in I2S and InS systems are calculated. The line shapes are predicted to comprise a single center line and "decoupling sidebands" on each side of the center line which move outward and diminish in amplitude as the decoupling field is increased. The predicted behavior is confirmed by experiments on an isolated seven spin system, where the decoupling sidebands are observed directly, and some organic solids in which the decoupling sidebands are not observed directly but in which their presence can be deduced from the behavior of the center line. A comparison is made between the theoretical predictions based on a complete quantum mechanical treatment and the predictions made using classical approximations in the model for the line shape. We conclude, based on our experimental results, that the line shape has a character which reflects the quantum nature of the spin system, even it? organic solids, and that on-resonance terms appear to dominate experimental line shapes.