Editing a simple curve This is such a dumb question, I'm embarrassed to ask - but I cannot figure out how to modify this simple shape. 

The shape comprises a 'fancy' head and tail connected by two straight segments. 

All I want to do is add a control point to each of the straight segments so that they can deform along the x-axis - but the deformation should only affect the middle bit. The parts above and below the dashed lines would be unaffected by the deformation.

The parameters for deforming the respective straight sections gets more complicated, and I've added an example of some unacceptable deformations, but really that's a question for another day...
Another way is to use only Bezier curves for the whole shape.
You can use the handles to adjust the faloff - sharp/gradual.



Here is the .blend
(updated 16:40 - matched more precisely to the original + works properly with bevel)