Unreliable failure detectors are a well known means to enrich asynchronous distributed systems with time-free semantics that allow to solve consensus in the presence of crash failures. Implementing unreliable failure detectors requires a system that provides some synchrony, typically an upper bound on end-to-end message delays. Recently, we introduced an implementation of the perfect failure detector in a novel partially synchronous model, referred to as the Θ-Model, where only the ratio Θ of maximum vs. minimum end-to-end delay of messages that are simultaneously in transit must be known a priori (while the actual delays need not be known and not even be bounded). In this paper, we present an alternative failure detector algorithm, which is based on a clock synchronization algorithm for the Θ-Model. It not only surpasses our first implementation with respect to failure detection time, but also works during the system booting phase.