A carousel is a computer-controlled warehousing system, which is widely used to store small- and medium-sized goods. One of the most important performance characteristics of such systems is the pick time of an order, which mostly depends on the travel time of the carousel. In this article, we consider some reasonable heuristics for order picking. In particular, we establish properties of the Nearest Item (NI) heuristic. This one is frequently used in practice. We derive tight upper bounds for the travel time under the NI heuristic and closed-form expressions for its mean and variance. We also present a simple two-moment approximation for the distribution of the travel time. In addition, we find the mean, variance, and distribution for the number of turns.