A number of studies have shown that rainfall processes may be described by stochastic scaling models in the time domain. However, most of the data sets have a resolution that is too limited to perceive the internal structure and variability of rain events. In this study, we analyze high-resolution (15 s) disdrometer time series, of total duration 2 years, obtained in Palaiseau, France. Monofractal and multifractal analysis tools are applied to the data set in order to investigate the scaling properties of the process, especially within the framework of universal multifractals (UMs). From spectral analysis and first-order structure function, it is shown that rainfall should be modeled by nonconservative (integrated) processes at small scales (hourly or finer) but not at larger scales. Multifractal analysis shows that two multiscaling regimes should be distinguished, i.e., ∼3 days to 30 min and 15 min to 15 s, with different UM parameters. The former is likely to represent the interevent variability, and the latter is likely to represent the event internal variability. Moreover, most data points contain zero values, which are susceptible to bias multifractal analysis results. In order to assess the effect of the zeros on multifractal analysis results, the UM parameters are also estimated from two variants: from uninterrupted rain events (with almost no zeros) and from a modified (weighted) version of analysis procedure that overweights nonzero values. The parameters are shown to depend noticeably on the proportion of zeros. We propose an approach based on a scaling support of the time series and derive semitheoretical formulas for the bias in the parameters, which are applied in our case study. Finally, we discuss the advantages and drawbacks of some models for numerical simulation of multifractal fields containing a lot of zeros.