I need to know what kind to order for my vessel sink.

Wow. Didn't know this was such a hard question. Thought SOMEbody out there would know!

The pop up without overflow is much shallower. As you can see in this image Kohler K-7124-BRZ Pop-Up Clicker Drain without Overflow in Oil Rubbed (http://www.google.com/products/catalog?hl=en&q=pop+up+drain+with+over+flow&um=1&ie=UTF-8&cid=6222006544690685275&sa=X&ei=EmaTTaL7AtO50QGwheDMBw&ved=0CC4Q8gIwBQ#) there are pval openings below the ring to allow over flow to get back into the drain passed the seal of the pop up. Here is the same drain without over flow http://www.google.com/products/catalog?hl=en&q=pop+up+drain+without+over+flow&um=1&ie=UTF-8&cid=15460538513770056256&sa=X&ei=d2aTTcKAPOjp0gHQveTMBw&ved=0CEQQ8gIwBA#