This study considers the staffing problem of a vendor call center in a co-sourcing setting. The aim is to take short-term variability and correlations in time for call arrivals at such a vendor call center into account. To do so, peakedness is proposed as a useful measure of the burstiness in the arrival stream. The study empirically demonstrates the presence of bursty arrivals at a call center and proposes an approach to the measurement of the peakedness of the arrival stream making use of standard call center data. The problematic nature of bursty arrivals in the context of call center co-sourcing is demonstrated along with an asymptotic result establishing that the problem persists in large call centers. The study then analyzes two peakedness-based staffing methods: one which is a well known extension of the square root staffing rule and another which makes use of the Hayward approximation principles. Both approaches are simple and enable the vendor to improve its staffing procedure with good accuracy.