The good thing about Tug Boat style boats is that more of the weight is below the waterline.  Although not recommended they can even recover after going sideways under a bridge.

 

The following is from http://www.onr.com/user/rleo/More/towboat.htm, more info about this is at http://www.phule.net/mirrors/towboat-history.html

 

River transportation is filled with the potential for serious injury or death. Nowhere is this more evident than in the following series of photos taken on the Tombigee river in 1979.

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On April 28, 1979 towboat CAHABA, under the command of Capt. Jimmy Wilkerson, was dropping 2 barges thru the east span of Rooster Bridge on the Tombigee River (mile marker 200), with intent of running the boat around thru the lift span and catching the barges downstream of the bridge (for the why of this, see the following note). Pilot Earl Barnhart and two deckhands were placed on the tow to cast off the safety wires and winch wires.