Recent results in end-to-end automatic speech recognition have demonstrated the efficacy of pseudo-labeling for semi-supervised models trained both with Connectionist Temporal Classification (CTC) and Sequence-to-Sequence (seq2seq) losses. Iterative Pseudo-Labeling (IPL), which continuously trains a single model using pseudo-labels iteratively re-generated as the model learns, has been shown to further improve performance in ASR. We improve upon the IPL algorithm: as the model learns, we propose to iteratively re-generate transcriptions with hard labels (the most probable tokens), that is, without a language model. We call this approach Language-Model-Free IPL (slimIPL) and give a resultant training setup for low-resource settings with CTC-based models. slimIPL features a dynamic cache for pseudo-labels which reduces sensitivity to changes in relabeling hyperparameters and results in improved training stability. slimIPL is also highly-efficient and requires 3.5-4x fewer computational resources to converge than other state-of-the-art semi/self-supervised approaches. With only 10 hours of labeled audio, slimIPL is competitive with self-supervised approaches, and is state-of-the-art with 100 hours of labeled audio without the use of a language model both at test time and during pseudo-label generation.