Curved Typography with illustrator

Question

I am trying to reproduce the great Ivan Chermayeff et Thomas Geismar Guggeinheim poster with Adobe Illustrator CS5 without any success. I am trying to distort my text with envelop tool; I made a shape and distort my text with the shape.

My attempts:

Answer 1

Since the original shape is simple, you could use Illustrator's primitive 3D tools to create the shape and map the text to it.

Steps

1. Create your text objects (two in this case), create Symbols out of them
2. Draw a half slice of the 3D object, apply a Fill to it (but no Stroke)
3. Apply Effect > 3D > Revolve... to your Slice, tweak the rotations to your liking
4. Use Map Art to position your text symbols on the faces of the 3D shape
5. Drop the Opacity of the Fill on the 3D object to 0%

Demo

Here's a comparison to the original after some additional tweaking:

Answer 2

Set your text, select it and then go to Object > Envelope Distort > Make with Mesh. Set a 1 x 1 mesh and then adjust the position of the corner points and the direction of the handles on the corners to get the curve that you want.

Something like this...

Generally, when you want nice smooth curves, use as few control points a possible.