The generalized likelihood ratio (GLR) method is a recently introduced gradient estimation method for handling discontinuities for a wide scope of sample performances. We put the GLR methods from previous work into a single framework, simplify regularity conditions for justifying unbiasedness of GLR, and relax some of those conditions that are difficult to verify in practice. Moreover, we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance. Numerical experiments show that the variance reduction could be significant in various applications.