Storming Mudbrick fortifications

How did early bronze-age armies assault fortified towns?  And by early, I mean before the rise of Assyria.  The difficulties, as I see it, are multi-pronged: 

1.  The lack of effective seige engines

2.  Poor logistics or no logistics prevents long standing seiges

3.  Existence of Long range missile weapons (composite bow, heavy sling)

Obviously these challenges were overcome, since the world's first great empires were formed during this period....but the question is how?