We present LAFTER, an algorithm for de-noising single particle reconstructions from cryo-EM. Single particle analysis entails the reconstruction of high-resolution volumes from tens of thousands of particle images with low individual signal-to-noise. Imperfections in this process result in substantial variations in the local signal-to-noise ratio within the resulting reconstruction, complicating the interpretation of molecular structure. An effective local de-noising filter could therefore improve interpretability and maximise the amount of useful information obtained from cryo-EM maps. LAFTER is a local de-noising algorithm based on a pair of serial real-space filters. It compares independent half-set reconstructions to identify and retain shared features that have power greater than the noise. It is capable of recovering features across a wide range of signal-to-noise ratios, and we demonstrate recovery of the strongest features at Fourier shell correlation (FSC) values as low as 0.144 over a 2563-voxel cube. A fast and computationally efficient implementation of LAFTER is freely available. We also propose a new way to evaluate the effectiveness of real-space filters for noise suppression, based on the correspondence between two FSC curves: 1) the FSC between the filtered and unfiltered volumes, and 2) Cref, the FSC between the unfiltered volume and a hypothetical noiseless volume, which can readily be estimated from the FSC between two half-set reconstructions.