Collapse is a good tool if you are wanting to work on a few different vertices, but using it on a large number of vertices is like performing cuticle surgery on an elephant.  Way to tedious.

Try using the "Weld" tool.  It does the same thing as collapse, but with a much more controlled system, and over a larger area.  To use it, select the object, go into sub-obj modification and select all the vertices.  Now scroll down the modifier command bar, and pay close attention.  About half-way down you should see a section called "weld" with a couple of buttons that read "selected" and "target" below it.

With all the vertices in the object selected, click "target" and change the number next to it to 1.  I'm not exactly sure what this does, but it has something to do with pixels, and if you want the object to stay the same shape, the smaller the pixel number the better.

Now highlight the number just above the pixel number.  This is the amount of space that can be aloud between vertices when you press the "selected" button.  If the vertices are closer than this number indicates, they'll be colapsed together.  Make this a small number.  I usually use something like 0.125", but you can use whatever you like.

Now press the "selected" button.  Continue pressing it until you get a message saying "no vertices within weld threshold".