Disclosed herein are exemplary embodiments of innovations in the area of encoding pictures or portions of pictures (e.g., slices, coding tree units, or coding units) and determining whether and how certain filtering operation should be performed and flagged for performance by the decoder in the bitstream. In particular examples, various implementations for setting the sample adaptive offset (SAO) syntax elements in the H.265/HEVC standard are disclosed. Although these examples concern the H.265/HEVC standard and its SAO filter, the disclosed technology is more widely applicable to other video codecs that involve filtering operations (particularly multi-stage filtering operations) as part of their encoding and decoding processes.