CSLTA is a stochastic temporal logic for continuous-time Markov chains (CTMC) where formulas similarly to those of CTL* are inductively defined by nesting of timed path formulas and state formulas. In particular a timed path formula of CSLTA is specified by a single-clock Deterministic Timed Automaton (DTA). Such a DTA features two kinds of transitions: synchronizing transitions triggered by CTMC transitions and autonomous transitions triggered by time elapsing that change the location of the DTA when the clock reaches a given threshold. It has already been shown that CSLTA strictly includes stochastic logics like CSL and asCSL. An interesting variant of CSLTA consists in equipping transitions rather than locations by boolean formulas. Here we answer the following question: do autonomous transitions and/or boolean guards on transitions enhance expressiveness and/or conciseness of DTAs? We show that this is indeed the case. In establishing our main results we also identify an accurate syntactical characterization of DTAs for which the autonomous transitions do not add expressive power but lead to exponentially more concise DTAs.