Classical algorithms that were derived with Rayleigh clutter assumption yield increased false alarm rate under Weibull clutter. In this study, a method for radar thresholding in range-heterogeneous Weibull radar clutter is proposed. The method employs Expectation-Maximization (EM) algorithm in estimation of the parameters and sets the threshold according to these estimates to yield the desired false alarm rate. Due to the mathematical complexity of the shape parameter estimation, an algorithm that uses a predefined shape parameter set is proposed. Performance of the algorithm is analyzed and it is shown to perform successfully even under spiky clutter conditions.