Observations of gamma-ray burst (GRB) afterglows have long provided the most detailed information about the origin of this spectacular phenomenon. The model that is most commonly used to extract physical properties of the event from the observations is the relativistic fireball model, where ejected material moving at relativistic speeds creates a shock wave when it interacts with the surrounding medium. Electrons are accelerated in the shock wave, generating the observed synchrotron emission through interactions with the magnetic field in the downstream medium. It is usually assumed that the accelerated electrons follow a simple power-law distribution in energy between specific energy boundaries, and that no electron exists outside these boundaries. This Letter explores the consequences of adding a low-energy power-law segment to the electron distribution with energy that contributes insignificantly to the total energy budget of the distribution. The low-energy electrons have a significant impact on the radio emission, providing synchrotron absorption and emission at these long wavelengths. Shorter wavelengths are affected through the normalization of the distribution. The new model is used to analyze the light curves of GRB 990510, and the resulting parameters are compared to a model without the extra electrons. The quality of the fit and the best-fit parameters are significantly affected by the additional model component. The new component is in one case found to strongly affect the X-ray light curves, showing how changes to the model at radio frequencies can affect light curves at other frequencies through changes in best-fit model parameters.