Spectral-estimation OCT (SE-OCT) is a computational method to enhance the axial resolution beyond the traditional bandwidth limit. However, it has not yet been used widely due to its high computational load, dependency on user-optimized parameters, and inaccuracy in intensity reconstruction. In this study, we implement SE-OCT using a fast implementation of the iterative adaptive approach (IAA). This non-parametric spectral estimation method is optimized for use on OCT data. Both in simulations and experiments we show an axial resolution improvement with a factor between 2 and 10 compared to standard discrete Fourier transform. Contrary to parametric methods, IAA gives consistent peak intensity and speckle statistics. Using a recursive and fast reconstruction scheme the computation time is brought to the sub-second level for a 2D scan. Our work shows that SE-OCT can be used for volumetric OCT imaging in a reasonable computation time, thus paving the way for wide-scale implementation of super-resolution OCT.