We study a courier dispatching problem in an on-demand delivery system in which customers are sensitive to delay. Specifically, we evaluate the effect of temporal pooling by comparing systems using the dedicated strategy, with which only one order is delivered per trip, versus the pooling strategy, with which a batch of consecutive orders is delivered on each trip. We capture the courier delivery system’s spatial dimension by assuming that, following a Poisson process, demand arises at a uniformly generated point within a service region. With the same objective of revenue maximization, we find that the dispatching strategy depends critically on customers’ patience level, the size of the service region, and whether the firm can endogenize the demand. We obtain concise but informative results with a single courier and assuming that customers’ underlying arrival rate is large enough, meaning a crowded market, such as rush hour delivery. In particular, when the firm has a growth target and needs to achieve an exogenously given demand rate, using the pooling strategy is optimal if the service area is large enough to fully exploit the pooling efficiency in delivery. Otherwise, using the dedicated strategy is optimal. In contrast, if the firm can endogenize the demand rate by varying the delivery fee, using the dedicated strategy is optimal for a large service area. The reason is that it is optimal for the firm to sustain a relatively low demand rate by charging a high fee for a large service radius: within this large area, the pooling strategy leads to a long wait because it takes a long time for multiple orders to accumulate. Moreover, with an exogenous demand rate to meet, customers’ patience level has no impact on the dispatch strategy. However, when the demand rate can be endogenized, the dedicated strategy is preferable if customers are impatient. Furthermore, we extend our model to account for social welfare maximization, a hybrid contingent delivery policy, a general arrival rate that does not have to be large, a nonuniform distribution of orders in the service region, and multiple couriers. We also conduct numerical analysis and simulations to complement our main results and find that most insights in our base model still hold in these extensions and numerical studies.