For jointly estimating angle-Doppler information, two-dimensional MUSIC is often applied, which requires an exhaustive grid-search over angle-Doppler domain. To mitigate the computational complexity and enhance the estimation performance we modify two-dimensional MUSIC in three steps. First, instead of using two-dimensional spectral search, it is converted to two consecutive polynomial root-finding problem. Second, the degree of the polynomial in the first root-findingstage is undesirably high in general, hence we approximate it to a lower-order polynomial through DFT. Lastly further enhancement can be achieved by having the closest approximation of null spectrum function by assigning unequal weight coefficients. Cramer-Rao-bound is derived for joint angle-Doppler-estimation as a benchmark in our performance analysis.