Most modern approaches for domain adaptive semantic segmentation rely on continued access to source data during adaptation, which may be infeasible due to computational or privacy constraints. We focus on source-free domain adaptation for semantic segmentation, wherein a source model must adapt itself to a new target domain given only unlabeled target data. We propose Self-Supervised Selective Self-Training (S4T), a source-free adaptation algorithm that first uses the model's pixel-level predictive consistency across diverse views of each target image along with model confidence to classify pixel predictions as either reliable or unreliable. Next, the model is self-trained, using predicted pseudolabels for reliable predictions and pseudolabels inferred via a selective interpolation strategy for unreliable ones. S4T matches or improves upon the state-of-the-art in source-free adaptation on 3 standard benchmarks for semantic segmentation within a single epoch of adaptation.