CPUs routinely offload to NICs network-related processing tasks like packet segmentation and checksum. NIC offloads are advantageous because they free valuable CPU cycles. But their applicability is typically limited to layer=4 protocols (TCP and lower), and they are inapplicable to layer-5 protocols (L5Ps) that are built on top of TCP. This limitation is caused by a misfeature we call "offload dependence,"which dictates that L5P offloading additionally requires offloading the underlying layer=4 protocols and related functionality: TCP, IP, firewall, etc. The dependence of L5P offloading hinders innovation, because it implies hard-wiring the complicated, ever-changing implementation of the lower-level protocols. We propose "autonomous NIC offloads,"which eliminate offload dependence. Autonomous offloads provide a lightweight software-device architecture that accelerates L5Ps without having to migrate the entire layer=4 TCP/IP stack into the NIC. A main challenge that autonomous offloads address is coping with out-of-sequence packets. We implement autonomous offloads for two L5Ps: (i) NVMe-over-TCP zero-copy and CRC computation, and (ii) https authentication, encryption, and decryption. Our autonomous offloads increase throughput by up to 3.3x, and they deliver CPU consumption and latency that are as low as 0.4x and 0.7x, respectively. Their implementation is already upstreamed in the Linux kernel, and they will be supported in the next-generation of Mellanox NICs.