The use of high undersampling factors and short flip angle trains leads to shorter acquisition times in MR Fingerprinting acquisitions. To obtain accurate multi-component estimates from this data advanced reconstructions are required. We study a low-rank ADMM based reconstruction method that adds a multi-component constraint to the inverse reconstruction problem (MC-ADMM). This method is combined with a joint-sparsity constraint yielding higher quality multi-component estimates with k-SPIJN than with previous methods. In simulations we observed increased stability to sequence truncation and in vivo multi-component estimates contained less noise-like effects.