Illustrator :: Smooth Transition Of Stroke Width Along Line Segment While Preserving Original Width Outside

Trying to use the width tool, I ran into the following problem. I would like to have a smooth transition of the stroke width between two width points while keeping the original stroke width unchanged outside of that line segment.
 
There are four width points here: two end points and two in between. The original stroke width is 200. The two on the left have one side set to 100 while the two on the right have one side set to 50. I would like to eliminate the distortion of the line width occuring in the first and third line segments. The only solution that I have come up with so far is to place two additional width points very close to the two middle width points: one with a 100-unit side to the left of the second point in the picture and one with a 50-unit side to the right of the third point in the picture. Yet there will be a small distirtion in between.