Mitigation of gender bias in NLP has a long history tied to debiasing static word embeddings. More recently, attention has shifted to debiasing pre-trained language models. We study to what extent the simplest projective debiasing methods, developed for word embeddings, can help when applied to BERT’s internal representations. Projective methods are fast to implement, use a small number of saved parameters, and make no updates to the existing model parameters. We evaluate the efficacy of the methods in reducing both intrinsic bias, as measured by BERT’s next sentence prediction task, and in mitigating observed bias in a downstream setting when fine-tuned. To this end, we also provide a critical analysis of a popular gender-bias assessment test for quantifying intrinsic bias, resulting in an enhanced test set and new bias measures. We find that projective methods can be effective at both intrinsic bias and downstream bias mitigation, but that the two outcomes are not necessarily correlated. This finding serves as a warning that intrinsic bias test sets, based either on language modeling tasks or next sentence prediction, should not be the only benchmark in developing a debiased language model.