Cloud computing has emerged as a corner stone of today's computing landscape. More and more customers who outsource their infrastructure benefit from the manageability, scalability and cost saving that come with cloud computing. Those benefits get amplified by the trend towards microservices. Instead of renting and maintaining full VMs, customers increasingly leverage container technologies, which come with a much more lightweight resource footprint while also removing the need to emulate complete systems and their devices. However, privacy concerns hamper many customers from moving to the cloud and leveraging its benefits. Furthermore, regulatory requirements prevent the adaption of cloud computing in many industries, such as health care or finance. Standard software isolation mechanisms have been proven to be insufficient if the host system is not fully trusted, e.g., when the cloud infrastructure gets compromised by malicious third-party actors. Consequently, confidential computing is gaining increasing relevance in the cloud computing field. We present Trusted Container Extensions (TCX), a novel container security architecture, which combines the manageability and agility of standard containers with the strong protection guarantees of hardware-enforced Trusted Execution Environments (TEEs) to enable confidential computing for container workloads. TCX provides significant performance advantages compared to existing approaches while protecting container workloads and the data processed by them. Our implementation, based on AMD Secure Encrypted Virtualization (SEV), ensures integrity and confidentiality of data and services during deployment, and allows secure interaction between protected containers as well as to external entities. Our evaluation shows that our implementation induces a low performance overhead of 5.77% on the standard SPEC2017 benchmark suite.