In-Context Reinforcement Learning is an emerging field with great potential for advancing Artificial Intelligence. Its core capability lies in generalizing to unseen tasks through interaction with the environment. To master these capabilities, an agent must be trained on specifically curated data that includes a policy improvement that an algorithm seeks to extract and then apply in context in the environment. However, for numerous tasks, training RL agents may be unfeasible, while obtaining human demonstrations can be relatively easy. Additionally, it is rare to be given the optimal policy, typically, only suboptimal demonstrations are available. We propose $AD^{\epsilon}$, a method that leverages demonstrations without policy improvement and enables multi-task in-context learning in the presence of a suboptimal demonstrator. This is achieved by artificially creating a history of incremental improvement, wherein noise is systematically introduced into the demonstrator's policy. Consequently, each successive transition illustrates a marginally better trajectory than the previous one. Our approach was tested on the Dark Room and Dark Key-to-Door environments, resulting in over a $\textbf{2}$x improvement compared to the best available policy in the data.