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The accurate and efficient operation of many applications and protocols in wireless sensor networks require synchronized notion of time. To achieve network-wide time synchronization, a common strategy is to flood current time information of a reference node into the network, which is utilized by the de facto time-synchronization protocol Flooding Time-Synchronization Protocol (FTSP). In FTSP, the propagation speed of the flood is slow because each node waits for a given period of time to propagate its time information about the reference node. It has been shown that slow-flooding decreases the synchronization accuracy and scalability of FTSP drastically. Alternatively, rapid-flooding approach is proposed in the literature, which allows nodes to propagate time information as quickly as possible. However, rapid flooding is difficult and has several drawbacks in wireless sensor networks. In this paper, our aim is to reduce the undesired effect of slow-flooding on the synchronization accuracy without changing the propagation speed of the flood. Within this context, we realize that the smaller the difference between the speeds of the clocks, the smaller the undesired effect of waiting times on the synchronization accuracy. In the light of this realization, our main contribution is to show that the synchronization accuracy and scalability of slow-flooding can drastically be improved by employing a clock speed agreement algorithm among the sensor nodes. We present an evaluation of this strategy on a testbed setup including 20 MICAz sensor nodes. Our theoretical findings and experimental results show that employing a clock speed agreement algorithm among the sensor nodes drastically improves the synchronization accuracy and scalability of slow-flooding.