I cannot understand why these 5 1/2 s were so large.  I have had a host of exercise shoes which fit me very well and are a ladies 6.  I read that leather exercise shoes run large, so I ordered a 5 1/2.  They were falling off me.  I even tried an insole insert and thicker socks. ( I've even worn a Saucony before in a 5 1/2, a running shoe.  I didn't keep it long because it calloused my heels, so I gave them to my cousin and she loved them.)  So I sent the Saucony ProGrid Integrity back.  They did look like good quality shoes, though, so I hope someone can buy them and they will fit them.