The relationship between Q penalty (QP) and eye-closure penalty (ECP) is examined for distorted signals in the presence of signal-dependent noise. A simple model is developed to describe the behavior of return-to-zero (RZ) modulation formats and is compared with a model for nonreturn-to-zero (NRZ) formats. The accuracy of the analysis is investigated with extensive simulations, and the numerical results from analysis and simulation are found to be in generally good agreement. Experimental measurements of distortion caused by uncompensated dispersion also show agreement with the simulation results and model predictions. The simplified models allow a means to budget QPs from distortion effects in a straightforward manner during network design for different modulation formats. The analysis predicts a smaller Q penalty as a function of ECP for RZ modulation formats in comparison with NRZ and smaller relative penalties for RZ formats with narrower pulsewidths.