Curves: Can't seem to smooth bezier handles

Hello. Got a dilemma, hoping someone can drop me a hint.
In the shape above I want to smooth the bezier handles in the vertices of my Curve.
But “Smooth” doesn’t do it. Neither does changing the Handle Type. In fact nothing I do seems to let me smooth these out so the object becomes circle-like. I’m hoping there’s a simple answer.

Further details:
I can apply a Subsurf before converting to Curve, but the result of such a destructive edit is of course a high vert count, which means I have little control over the shape after that.
I will use this Curve as a Modifier, so it must be a Curve, cannot be left as a Mesh.

Thanks in advance for any advice.

Those are not bézier handles. There is “set spline type” button on the tool shelf in edit mode.

Thank you!
OK, I got the Spline Type set to Bézier now. But the shape has not changed. I want to clear the handle positions to smooth it out.

with the curve selected, all points highlighted, change them with V key from Vector to Aligned, at least that might help get them round.

I got best results with Auto. Still looking weird and wobbly. Will keep playing…