A Conditional Simple Temporal Network (CSTN) is a structure for representing and reasoning about time in domains where temporal constraints may be conditioned on outcomes of observations made in real time. A CSTN is dynamically consistent (DC) if there is a strategy for executing its time-points such that all relevant constraints will necessarily be satisfied no matter which outcomes happen to be observed. The literature on CSTNs contains only one sound-and-complete DC-checking algorithm that has been implemented and empirically evaluated. It is a graph-based algorithm that propagates labeled constraints/edges. A second algorithm has been proposed, but not evaluated. It aims to speed up DC checking by more efficiently dealing with so-called negative q-loops.This paper presents a new two-phase approach to DC-checking for CSTNs. The first phase focuses on identifying negative q-loops and labeling key time-points within them. The second phase focuses on computing (labeled) distances from each time-point to a single sink node. The new algorithm, which is also sound and complete for DC-checking, is then empirically evaluated against both pre-existing algorithms and shown to be much faster across not only previously published benchmark problems, but also a new set of benchmark problems. The results show that, on DC instances, the new algorithm tends to be an order of magnitude faster than both existing algorithms. On all other benchmark cases, the new algorithm performs better than or equivalently to the existing algorithms.