Signal level quantization, a fundamental component in digital sampling of continuous signals such as DPCM, or in near-lossless predictive-coding based compression schemes of digital data such as JPEG-LS, often produces visible banding artifacts in regions where the input signals are very smooth. Traditional techniques for dealing with this issue include dithering, where the encoder contaminates the input signal with a noise function (which may be known to the decoder as well) prior to quantization. We propose an alternate way for avoiding banding artifacts, where quantization is applied in an interleaved fashion, leaving a portion of the samples untouched, following a known pseudo-random Beroulli sequence. Our method, which is sufficiently general to be applied to other types of media, is demonstrated on a modified version of JPEG-LS, resulting in a significant reduction in visible artifacts in all cases, while producing a graceful degradation in compression ratio. Keywords : Predictive coding Dithering Quantization Near-lossless compression Image compression Work partially supported by the ANII DT program.