Fifteen lunar occultation events have been observed in the course of a program aimed at the measurement of angular diameters of southern near-infrared sources and the detection of possible circumstellar shells. As a result, angular diameters have been determined for the first time for nine stars with spectra cooler than K 5. We present the first practical implementation of a method for the removal of low-frequency fluctuations induced by atmospheric turbulence in occultation traces. Also, a detailed analysis is given of the limiting resolution set by our instrumentation and of the errors in the final results. The angular diameters are discussed in connection with available multi-wavelength photometry, obtained in part in the course of our observations, leading to direct estimates of the effective temperatures. We also suggest and discuss the presence of circumstellar shells around four sources with low effective temperatures and infrared excesses.