revolve with curve on top end

Hello, I'm pretty sure this can't be achieve with just a revolve feature, but I asked anyway.
I'm looking for a way to create a cone with variable high (design Table) and the top edge to follow a curves instead of being regular.
What should be used instead, a loft?
Using an another sketch to cut the curve will never be smooth on the intersection with he edge I'm afraid.
3 Answers

I did what I think you're asking about by:
-revolving a surface
-trimming it's top to achieve the desired curve
-adding ruled surface to curved edge to create the flange around the top, knitting it with the trimmed surface and blending them together with a fillet
-thickening the surface to create solid geometry
I skipped (forgot;-) making a design table to drive the height, but that's simple enough.
Maybe this gives you some inspiration. There are probably other ways, such as lofting as you have mentioned, but this seemed the most straightforward to my tired-from-the-day brain.

Done in no time where I will have done it in half a day, Respect. Still have to deal with the design table, but I've been able to do it on a single sketch so I guess I will be able to do it on top of other Feature as well.
I really need to practice more often SW. But with illustrator, photoshop, 3Dsmax/vray... that's a lot to master, on top of usual daytime staff, I wish I had eternity to learn all of it.
I believe this is the easiest way:
1) Start a 3D sketch
2) Convert the outer or inner edge (using "Convert Entities")
3) Start a 2D sketch on a plane normal to the 3D sketch (Front or Right plane)
4) Draw half a circle with the opening downwards
5) Draw lines to connect the semi-circle with the top and side of the revolve
6) Make a Swept cut