Sequential sensing algorithms are developed for OFDM-based hierarchical cognitive radio (CR) systems. Secondary users sense multiple sub-bands simultaneously for possible spectrum availabilities under hard miss-detection constraints to prevent interference to the primary users. Accounting for the fact that the sensing time overhead can often be significant, a performance metric is developed based on the effective achievable data rate. An optimization problem is formulated in the framework of optimal stopping problems to maximize the average effective data rate by determining the best time to stop taking samples for sensing, as well as the best set of channels to use for data transmission. A basis expansion-based sub-optimal algorithm is derived to reduce the prohibitive complexity of the optimal solution.