Cartesian sub-sampling patterns play a major role in routine MRI, usually reconstructed using GRAPPA or SENSE and image based regularization. Coil compression is commonly applied to reduce computational load and noise. Software coil compression achieves only mediocre compression factors without compromising signal. Geometrical/ESPIRiT coil-compression use fully-sampled axes, when availables, to improve compression factors without reducing signal or reconstruction level. In this work we present Aliased Coil Compression for Cartesian subsampling patterns, achieving optimal compression without any signal loss. The method is especially useful for alleviating fast image-domain regularization (compressed sensing or deep learning) for available sequences.