We present LibrettOS, an OS design that fuses two paradigms to simultaneously address issues of isolation, performance, compatibility, failure recoverability, and run-Time upgrades. LibrettOS acts as a microkernel OS that runs servers in an isolated manner. LibrettOS can also act as a library OS when, for better performance, selected applications are granted exclusive access to virtual hardware resources such as storage and networking. Furthermore, applications can switch between the two OS modes with no interruption at runtime. LibrettOS has a uniquely distinguishing advantage in that, the two paradigms seamlessly coexist in the same OS, enabling users to simultaneously exploit their respective strengths (i.e., greater isolation, high performance). Systems code, such as device drivers, network stacks, and file systems remain identical in the two modes, enabling dynamic mode switching and reducing development and maintenance costs. To illustrate these design principles, we implemented a prototype of LibrettOS using rump kernels, allowing us to reuse existent, hardened NetBSD device drivers and a large ecosystem of POSIX/BSD-compatible applications. We use hardware (VM) virtualization to strongly isolate different rump kernel instances from each other. Because the original rumprun unikernel targeted a much simpler model for uniprocessor systems, we redesigned it to support multicore systems. Unlike kernel-bypass libraries such as DPDK, applications need not be modified to benefit from direct hardware access. LibrettOS also supports indirect access through a network server that we have developed. Instances of the TCP/IP stack always run directly inside the address space of applications. Unlike the original rumprun or monolithic OSes, applications remain uninterrupted even when network components fail or need to be upgraded. Finally, to efficiently use hardware resources, applications can dynamically switch between the indirect and direct modes based on their I/O load at run-Time. We evaluate LibrettOS with 10GbE and NVMe using Nginx, NFS, memcached, Redis, and other applications. LibrettOS's performance typically exceeds that of NetBSD, especially when using direct access.