The fluctuation experiment, devised by Luria and Delbrück in 1943, remains the method of choice for measuring microbial mutation rates in the laboratory. While most inference problems commonly encountered in a fluctuation experiment can be tackled by existing standard algorithms, investigators from time to time run into nonstandard problems not amenable to any existing algorithms. A major obstacle to solving these nonstandard problems is the construction of confidence intervals for mutation rates. This note describes methods for two important categories of nonstandard problems, namely, pooling data from separate experiments and analyzing grouped mutant count data, focusing on the construction of likelihood ratio confidence intervals. In addition to illustrative examples using real-world data, simulation results are presented to help assess the proposed methods.