With the prevalence of online platforms, today, data is being generated and accessed by users at a very high rate. Besides, applications such as stock trading or high frequency trading require guaranteed low delays for performing an operation on a database. It is consequential to design databases that guarantee data insertion and query at a consistently high rate without introducing any long delay during insertion. In this paper, we propose Nested B-trees (NB-trees), an index that can achieve a consistently high insertion rate on large volumes of data, while providing asymptotically optimal query performance that is very efficient in practice. Nested B-trees support insertions at rates higher than LSM-trees, the state-of-the-art index for insertion-intensive workloads, while avoiding their long insertion delays and improving on their query performance. They approach the query performance of B-trees when complemented with Bloom filters. In our experiments, NB-trees had worst-case delays up to 1000 smaller than LevelDB, RocksDB and bLSM, commonly used LSM-tree data-stores, could perform queries more than 4 times faster than LevelDB and 1.5 times faster than bLSM and RocksDB, while also outperforming them in terms of average insertion rate.