This paper introduces a finite memory compactor called convolutional compactor that provides compaction ratios of test responses in excess of 100x even for a very small number of outputs. This is combined with the capability to detect multiple errors, handling of unknown states, and the ability to diagnose failing scan cells directly from compacted responses. A convolutional compactor can be easily configured into a MISR that preserves most of these properties. Experimental results demonstrate the efficiency of compaction for several industrial circuits.