Recent work in zero-shot listwise reranking using LLMs has achieved state-of-the-art results. However, these methods are not without drawbacks. The proposed methods rely on large LLMs with billions of parameters and limited context sizes. This paper introduces LiT5-Distill and LiT5-Score, two methods for efficient zero-shot listwise reranking, leveraging T5 sequence-to-sequence encoder-decoder models. Our approaches demonstrate competitive reranking effectiveness compared to recent state-of-the-art LLM rerankers with substantially smaller models. Through LiT5-Score, we also explore the use of cross-attention to calculate relevance scores to perform reranking, eliminating the reliance on external passage relevance labels for training. We present a range of models from 220M parameters to 3B parameters, all with strong reranking results, challenging the necessity of large-scale models for effective zero-shot reranking and opening avenues for more efficient listwise reranking solutions. We provide code and scripts to reproduce our results at https://github.com/castorini/LiT5.