AI assistants for coding are on the rise. However one of the reasons developers and companies avoid harnessing their full potential is the questionable security of the generated code. This paper first reviews the current state-of-the-art and identifies areas for improvement on this issue. Then, we propose a systematic approach based on prompt-altering methods to achieve better code security of (even proprietary black-box) AI-based code generators such as GitHub Copilot, while minimizing the complexity of the application from the user point-of-view, the computational resources, and operational costs. In sum, we propose and evaluate three prompt altering methods: (1) scenario-specific, (2) iterative, and (3) general clause, while we discuss their combination. Contrary to the audit of code security, the latter two of the proposed methods require no expert knowledge from the user. We assess the effectiveness of the proposed methods on the GitHub Copilot using the OpenVPN project in realistic scenarios, and we demonstrate that the proposed methods reduce the number of insecure generated code samples by up to 16\% and increase the number of secure code by up to 8\%. Since our approach does not require access to the internals of the AI models, it can be in general applied to any AI-based code synthesizer, not only GitHub Copilot.