Least Squares Support Vector Machines (LS-SVMs) were proposed by replacing the inequality constraints inherent to L1-SVMs with equality constraints. So far this idea has only been suggested for a least squares (L2) loss. We describe how this can also be done for the sumof-slacks (L1) loss, yielding a new classifier (Least 1-Norm SVMs) which gives similar models in terms of complexity and accuracy and that may also be more robust than LS-SVMs with respect to outliers.