Infilling certain frame bays with RC is popular as a seismic rehabilitation technique. Unless the connection between the old concrete to the new ensures monolithic behavior, this technique is not covered by codes. To avoid penalizing the foundation of the new wall with a very high moment demand, the new concrete should not be thicker than the old frame members. A cost-effective connection of these members to a thin new web is proposed, with design and detailing conforming to current codes for new structures. For practical reasons footings of added walls are often small and weakly connected to the others; so, they uplift and rock during earthquakes. A model is proposed for uplifting footings in 3D, comprising two pairs of nonlinear-elastic springs in a cross layout. It is applied for nonlinear static or dynamic analyses of three buildings with added walls. Analyses of a prototype, regular 4-storey building show the benefits from uplift to the added walls and certain adverse effects on some columns, as well as the lack of a clear positive effect of adding tie-beams. Applications to a 7- and a 2-storey real building with extreme but typical irregularities exemplify the real-life restrictions in the use of added walls and show their limits for the improvement of seismic performance; certain deficiencies in flexure or shear remain in both buildings and are corrected at very low cost with local FRP jackets without new analysis of the building.