Everything Mayonnaise says is spot on. Holding your line is key, smoothness is just as important.
From the USCF 2006 Rulebook:
Section 1J3(b): For road races, only a bicycle with a freewheel and one working brake on each wheel shall be used, except as allowed elsewhere in these rules.
...the exception being:
Section 3E2 (under the heading "Individual Time Trial"): Road bicycles shall be used. Bicycles with a front hand brake and fixed wheel may also be used.