The standard FOSLS Method only works well if the exact solution of the problem is in H^2. For many practical applications of Stokes or Elasticity this is not true (Mixed BCs, reentrant corners, etc.). In our talk we present the FOSLL* Method, which is an FOSLS-like method, constructed to overcome this drawback. We will present numerical results for Stokes and linear Elasticity, which show optimal FE- and MG-convergence of the method.