Sentence Compression is the task of generating a shorter, yet grammatical, version of a given sentence, preserving the essence of the original sentence. This paper proposes a Black-Box Optimizer for Compression (B-BOC): given a black-box compression algorithm and assuming not all sentences need be compressed – find the best candidates for compression in order to maximize both compression rate and quality. Given a required compression ratio, we consider two scenarios: (i) single-sentence compression, and (ii) sentences-sequence compression. In the first scenario our optimizer is trained to predict how well each sentence could be compressed while meeting the specified ratio requirement. In the latter, the desired compression ratio is applied to a sequence of sentences (e.g., a paragraph) as a whole, rather than on each individual sentence. To achieve that we use B-BOC to assign an optimal compression ratio to each sentence, then cast it as a Knapsack problem which we solve using bounded dynamic programming. We evaluate B-BOC on both scenarios on three datasets, demonstrating that our optimizer improves both accuracy and Rouge-F1-score compared to direct application of other compression algorithms.