A major drawback of modern neural OpenIE systems and benchmarks is that they prioritize high coverage of information in extractions over compactness of their constituents. This severely limits the usefulness of OpenIE extractions in many downstream tasks. The utility of extractions can be improved if extractions are compact and share constituents. To this end, we study the problem of identifying compact extractions with neural-based methods. We propose CompactIE, an OpenIE system that uses a novel pipelined approach to produce compact extractions with overlapping constituents. It first detects constituents of the extractions and then links them to build extractions. We train our system on compact extractions obtained by processing existing benchmarks. Our experiments on CaRB and Wire57 datasets indicate that CompactIE finds 1.5x-2x more compact extractions than previous systems, with high precision, establishing a new state-of-the-art performance in OpenIE.