More and more people interact with their mobile phone while walking. The presented research analyzes; firstly, the negative effect of walking when considering reading and target selection tasks, such as weaker performance and higher workload. Here, we focused on one-handed interaction with a touch screen whereby the thumb is used as the input device. Secondly, we analyze how these negative effects can be compensated by increasing the text size and the size of the targets to select on the mobile phone. A comparative user study was conducted with 16 participants who performed target acquisition and reading tasks while standing and walking. The results show that whilst performance decreases, cognitive load increases significantly when reading and selecting targets when walking. Furthermore, the results show that the negative effect regarding target selection can be compensated by increasing the target size, but the text reading task did not yield better performance results for a larger text size due to the increased demand for scrolling. These results can be used to inform future designs of mobile user interfaces which might provide a dedicated walking mode.