Timed process algebra \(\text{TACS}^{\text{LT}}\), which conservatively extends Milner's CCS by permitting the specification of lower time bounds for the execution of actions and processes, is introduced. The faster-than preorder, introduced by Moller and Tofts (MT-preorder for short), is recalled. It is proved that the MT-preorder is a precongruence for all \(\text{TACS}^{\text{LT}}\) operators (including recursion). An amortized faster-than preorder is introduced and it is proved that the MT-preorder is fully abstract with respect to this preorder. A sound and complete axiomatization of the MT-preorder for the class of finite processes is given. The MT-preorder is investigated also for the case that internal (unobservable) actions are abstracted.