SU (4) POTENTIALS IN THE FAT-CENTER-VORTICES MODEL INVOLVE THREE VORTICES THAT TWO OF THEM ARE INDEPENDENT. USING THE SECOND VORTEX IN THE CALCULATIONS ONLY AFFECTS THE POTENTIALS OF LARGE DISTANCES AND DOESN'T HAVE AN IMPORTANT EFFECT AT INTERMEDIATE DISTANCES. THE LINEAR REGIME GETS LARGER BY INCREASING THE VORTEX CORE SIZE AND THE SLOPE OF EACH POTENTIAL TO THAT OF THE FUNDAMENTAL ONE IS QUALITATIVELY IN AGREEMENT WITH BOTH CASIMIR SCALING AND FLUX- TUBE COUNTING.