Commonly used disdrometers tend not to accurately measure concentrations of very small drops in the raindrop size distribution (DSD), either through truncation of the DSD at the small-drop end or because of large uncertainties on these measurements. Recent studies have shown that, as a result of these inaccuracies, many if not most ground-based disdrometers do not capture the "drizzle mode" of precipitation, which consists of large concentrations of small drops and is often separated from the main part of the DSD by a shoulder region. We present a technique for reconstructing the drizzle mode of the DSD from "incomplete" measurements in which the drizzle mode is not present. Two statistical moments of the DSD that are well measured by standard disdrometers are identified and used with a double-moment normalized DSD function that describes the DSD shape. A model representing the double-moment normalized DSD is trained using measurements of DSD spectra that contain the drizzle mode obtained using collocated Meteorological Particle Spectrometer and 2D video disdrometer instruments. The best-fitting model is shown to depend on temporal resolution. The result is a method to estimate, from truncated or uncertain measurements of the DSD, a more complete DSD that includes the drizzle mode. The technique reduces bias on low-order moments of the DSD that influence important bulk variables such as the total drop concentration and mass-weighted mean drop diameter. The reconstruction is flexible and often produces better rain-rate estimations than a previous DSD correction routine, particularly for light rain.