Reranking methods in machine translation aim to close the gap between common evaluation metrics (e.g. BLEU) and maximum likelihood learning and decoding algorithms. Prior works address this challenge by training models to rerank beam search candidates according to their predicted BLEU scores, building upon large models pretrained on massive monolingual corpora -- a privilege that was never made available to the baseline translation model. In this work, we examine a simple approach for training rerankers to predict translation candidates' BLEU scores without introducing additional data or parameters. Our approach can be used as a clean baseline, decoupled from external factors, for future research in this area.