Compressed Last-Level Cache (LLC) architectures have been proposed to enhance system performance by efficiently increasing the effective capacity of the cache, without physically increasing the cache size. In a compressed cache, the cacheline size varies depending on the achieved compression ratio. We observe that this size information gives a useful hint when selecting a victim, which can lead to increased cache performance. However, no replacement policy tailored to compressed LLCs has been investigated so far. This paper introduces the notion of size-aware compressed cache management as a way to maximize the performance of compressed caches. Toward this end, the Effective Capacity Maximizer (ECM) scheme is introduced, which targets compressed LLCs. The proposed mechanism revolves around three fundamental principles: Size-Aware Insertion (SAI), a Dynamically Adjustable Threshold Scheme (DATS), and Size-Aware Replacement (SAR). By adjusting the eviction criteria, based on the compressed data size, one may increase the effective cache capacity and minimize the miss penalty. Extensive simulations with memory traces from real applications running on a full-system simulator demonstrate significant improvements compared to compressed cache schemes employing the conventional Least-Recently Used (LRU) and Dynamic Re-Reference Interval Prediction (DRRIP)  replacement policies. Specifically, ECM shows an average effective capacity increase of 15% over LRU and 18.8% over DRRIP, an average cache miss reduction of 9.4% over LRU and 3.9% over DRRIP, and an average system performance improvement of 6.2% over LRU and 3.3% over DRRIP.