Shrinking tube or bending a cone I would like to make curved cone (I'm making 3D model of this dialog bubbles and I want to use curved cones to make line between the bubble and speaker. 

During my research I found, that I can either make cone and then curve it according to a bezier curve, or I can make path, use circle as its bevel object and then shrink it using taper object as described in this video.

Both approaches have problems. With the first approach it is extremely hard to bend the cone the way I want and I can't get proper results. The other approach is works well, when the path is straight. If the path is curved, then after the taper object the tube disappears.

What would be the good way to do that? I would very much prefer the path and bevel objects approach, because it does almost exactly what I need.
EDIT

To create a bent conical object. Start with a Curve and a Bezier Circle (Add Curve->Circle) as Bevel object:



Then change the Radius for the control points of the curve:



Other Ideas:

Do the whole object as a curve:



then fill it as a 2D



Then add a bevel:



If you add a Curve->Circle as a bevel Object you can so something like this: