Satellite radar altimeter observations are key to advanced studies in ocean dynamics, particularly those focusing on mesoscale processes. To resolve scales below about 100 km, because altimeter measurements are often characterized by a low signal-to-noise ratio (SNR), low-pass filtering or least-squares curve fitting is generally applied to smooth the data before analysis. Here, we present an alternative method. It is based on Empirical Mode Decomposition (EMD) developed to analyze non-stationary and non-linear processes, which adaptively projects a signal on a basis of empirical AM/FM functions called Intrinsic Modulation Functions (IMFs). Applied to a Gaussian noise signal, the EMD provides a set of IMFs with a predictable distribution of noise energy that can be exploited by wavelet-inspired threshold methods to provide an efficient approach to data denoising. The EMD method performs a local analysis of the SNR, does not require a priori assumptions about the underlying geophysical signal, e.g., its degree of smoothness or its compliance with a particular mathematical framework. The signal is simply assumed to be the sum of a piecewise-smooth deterministic part and a stochastic part. The proposed EMD-based denoising approach is therefore well suited for mapping non-linear features, such as strong gradients, and extreme values without significant smoothing. Using Jason-2, Cryosat-2, and Saral/AltiKa significant wave height measurements, the method provides an effective means of mapping overlooked geophysical variability of sea state at scales between about 100 km and 25 km, a range largely impacted by low SNR. Below 25 km, a spectral hump caused by inhomogeneities in the altimeter footprint essentially dominates the signal. In addition, the EMD method provides a consistent approach for long-term noise analysis and monitoring under global and local conditions. The proposed method is a step forward that will enable better exploitation of the unique set of altimeter observations that now covers more than 25 years.