Convolutional neural networks have been successful lately enabling companies to develop neural-based products, which demand an expensive process, involving data acquisition and annotation; and model generation, usually requiring experts. With all these costs, companies are concerned about the security of their models against copies and deliver them as black-boxes accessed by APIs. Nonetheless, we argue that even black-box models still have some vulnerabilities. In a preliminary work, we presented a simple, yet powerful, method to copy black-box models by querying them with natural random images. In this work, we consolidate and extend the copycat method: (i) some constraints are waived; (ii) an extensive evaluation with several problems is performed; (iii) models are copied between different architectures; and, (iv) a deeper analysis is performed by looking at the copycat behavior. Results show that natural random images are effective to generate copycats for several problems.