Subsurf text problem

I’ve been modelling a Chinese pagoda name plate lately. Working on this I saw the need of subdividing the chinese text. I created the text, converted it into mesh, and then applied the subsurf modifier. As a result of the triangulation, the result was really bad. I then tried to do a limited dissolve of the mesh, and then subdivide it. Again, with an unpleasing result. My last effort was to not convert the text, but rather keep it in its text format, and use the extrude and bevel function. This looked a lot better, but the beveling obviously leaves a flat surface on the top, and only smoothes the edges. This is not what I’m looking for.

To illustrate my points, I’ve attached a image. From top to bottom; Text with extrude + bevel, limited dissolved text mesh, modelled letter “E” with subsurf modifier to show what I am trying to achieve.
Is it even possible to subdivide a text mesh and get the result that I got on the “E”? If so, how?