Withdrawing Logic Willingly

Yesterday Blair announced U.K. troops reduction in Iraq. Today the Italian government fell over the issue of U.S. bases in Italy (http://www.cnn.com/2007/WORLD/europe/02/21/italy.vote.reut/index.html) and general foreign policy issues. The Table given at http://en.wikipedia.org/wiki/Multinational_force_in_Iraq lists the number of troops from each of the participants in the coalition of the willing (initially there were 49 countries then one withdrew leaving 48 including Afghanistan. 40 committed troops. The lowest number was two with some others at sub hundred level. 16 have completely withdrawn). What is interesting is that U.K. has 21000 private military contractors (three times their actual number of forces). Denmark has also announced that it will withdraw (http://www.cnn.com/2007/WORLD/europe/02/21/denmark.iraq/).
In light of all this Cheney's comments (http://www.cbsnews.com/stories/2007/02/21/iraq/main2497651.shtml) on British withdrawal are rather funny. On one hand he wants to get the job done in Iraq and is in agreement that more troops should be sent there and on the other he is claiming that things are well in southern Iraq and therefore the British can withdraw. Is it not more reasonable to send them where more troops are needed rather than completely withdrawing?