It is well known that there are linear-space data structures for 2-D orthogonal range counting with worst-case optimal query time O(log n/ loglog n). We give an O(n log log n)-space adaptive data structure that improves the query time to O(log log n + log k/ log log n), where k is the output count. When k = O(1), our bounds match the state of the art for the 2-D orthogonal range emptiness problem [Chan et al., 2011]. We give an O(n log log n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1 + delta)-factor approximation to the count in O(log log n) time for any fixed constant delta >0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. Last, we consider the 1-D range selection problem, where a query in an array involves finding the kth least element in a given subarray. This problem is closely related to 2-D 3-sided orthogonal range counting. Recently, Jorgensen and Larsen [2011] presented a linear-space adaptive data structure with query time O(log log n + log k/ log log n). We give a new linear-space structure that improves the query time to O(1 + log k/log log n), exactly matching the lower bound proved by Jorgensen and Larsen.