Previous research addressed the potential problems of the hard-disk oriented design of DBMSs of flashSSDs. In this paper, we focus on exploiting potential benefits of flashSSDs. First, we examine the internal parallelism issues of flashSSDs by conducting benchmarks to various flashSSDs. Then, we suggest algorithm-design principles in order to best benefit from the internal parallelism. We present a new I/O request concept, called psync I/O that can exploit the internal parallelism of flashSSDs in a single process. Based on these ideas, we introduce B+-tree optimization methods in order to utilize internal parallelism. By integrating the results of these methods, we present a B+-tree variant, PIO B-tree. We confirmed that each optimization method substantially enhances the index performance. Consequently, PIO B-tree enhanced B+-tree's insert performance by a factor of up to 16.3, while improving point-search performance by a factor of 1.2. The range search of PIO B-tree was up to 5 times faster than that of the B+-tree. Moreover, PIO B-tree outperformed other flash-aware indexes in various synthetic workloads. We also confirmed that PIO B-tree outperforms B+-tree in index traces collected inside the Postgresql DBMS with TPC-C benchmark.