Reinforcement Learning with Human Feedback (RLHF) has revolutionized language modeling by aligning models with human preferences. However, the RL stage, Proximal Policy Optimization (PPO), requires over 3x the memory of Supervised Fine-Tuning (SFT), making it infeasible to use for most practitioners. To address this issue, we present a comprehensive analysis the memory usage, performance, and training time of memory-savings techniques for PPO. We introduce Hydra-RLHF by first integrating the SFT and Reward models and then dynamically turning LoRA "off" during training. Our experiments show: 1. Using LoRA during PPO reduces its memory usage to be smaller than SFT while improving alignment across four public benchmarks, and 2. Hydra-PPO reduces the latency per sample of LoRA-PPO by up to 65% while maintaining its performance. Our results demonstrate that Hydra-PPO is a simple and promising solution for enabling more widespread usage of RLHF.