Output-bit selection is a recently proposed test-response compaction approach that can effectively deal with aliasing, unknown-value, and low-diagnosis problems. This approach has been implemented using a single counter and a multiplexer without considering unknown values. Also, such an implementation may require the application of a pattern multiple times in order to observe all selected responses. In this paper, we present a multiple-counter-based architecture with a new selection algorithm that can avoid most unknown-values yet achieve high compaction ratio. The remaining small number of unknowns can then be dealt with using some simple masking logic. Experiments on IWLS'05 circuits show that even with 16% unknown responses, all unknown values can be handled with 88.92%93.21% response-volume reduction still achieved and only a moderate increase in test-application time.