In this paper we study the 1-bounded space of 2-dimensional bin pack- ing. A sequence of rectangular items arrive one at a time, and the follow- ing item arrives only after the packing of the previous one, which after being packed cannot be moved. The bin size is 1 1 and the width and height of the items are 1. The objective is to minimize the number of bins used to pack all the items. At any time there is only 1 active bin, and the previously closed bins cannot be used for any subsequent items. The new algorithm o ers an improvement of the previous best known 8:84-competitive algorithm to a 6:53-competitive, it also raises the lower bound from 2:5 to 2:^6.