Line-edge roughness (LER) has important impacts on the quality of semiconductor device performance, and power spectrum estimates are useful tools in characterizing it. These estimates are often obtained by taking measurements of many lines and averaging a classical power spectrum estimate from each one. While this approach reduces the uncertainty of the estimates, there are disadvantages to the collection of many measurements. We propose techniques with widespread application in other fields that simultaneously reduce data requirements and the uncertainty of LER power spectrum estimates over current approaches at the price of computational complexity. Multitaper spectral analysis uses an orthogonal collection of data windowing functions or tapers to obtain a set of approximately statistically independent spectrum estimates. The Welch overlapped segment averaging is an earlier approach to reduce the uncertainty of power spectrum estimates. There are known techniques to evaluate the uncertainty of power spectrum estimates. We simulate random rough lines using the Thorsos method.