Curve fitting with minimum oscilation

Hi! I've been researching curve interpolation algorithms for a while, and I have the following problem.
All the classic ones like cubic spline, hermite, catmull rom, etc add small oscilations near the control points, and I don't want this. Are there other curve-fitting algoritms that, no matter if they need more control points than 4, they don't produce such oscillations?

I'm not sure what you mean by oscillations in the curves -- perhaps you could provide a picture? In that regard, the Catmull-Rom spline should be pretty good and minimizing unnecessary curvature in the curve. Are you sure that it is not a problem with your implementation?

-Josh

So-called "natural" cubic splines (where the second derivative of contiguous segments matches at the common node and the second derivative at the ends is 0) have the least "curvature" among all interpolating curves, in some sense that can be made very precise (minimum integral of the square of the second derivative). So I would give them a try. If you are not happy with the results, you must have some other criterion in mind, so it would be good to see some examples.