You should be able to do this by using the Direct Select tool (open arrow) to adjust the anchor points/handles to make your traced path fit the curve better. Any reason why you cannot just use a copy of the original curve for your purpose?
... several paths in the sequence ...
It is better to have one continuous path.
A few hints on drawing, and adjusting while drawing, are presented in this recent thread:
Thank you, Larry and Jacob, for the speedy reply. Re Larry G. it would be helpful to detail the Direct Selection solution exactly, i.e. the process of manipulating anchor points and handles in this instance. OTOH I'm not sure what you mean by 'using a copy of the original curve'. This is in fact an a copy of the original curve from the software program that created it.
Jacob, surely you understand that creating an outline for the number '3' involves more than one continuous path or have I misunderstood? That's the issue I'm addressing in my question.
Can you show us a screen capture of the original and your attempt to follow the curve with the Pen tool. Curves are approximated by click/hold/dragging with the Pen tool. When you do this you will see a handle being extended from the anchor point. At each point as you follow the curve do the same. It's best to place the original on a layer by itself and lock the layer, then make another layer to work on. Use a different color for the two lines which will make it easier to distinguish. After you have drawn the new path you can adjust by using the Direct Select tool to click on an anchor point to adjust it. When you do the handles associated with that point should become visible. You can drag the handles by mousing down on the round end of the handle. You can move an anchor point by mousing down on the anchor point and dragging the point.
What I mean is if you use the Selection tool and try can you select the line from the original software?
Thanks, that was the answer. It takes some trial and error figuring where to position anchor points on an irregular curve such that the handles will align the bezier path exactly along the curve edge.