The Alpha algorithm was the first process discovery algorithm that was able to discover process models with concurrency based on incomplete event data while still providing formal guarantees. However, as was stated in the original paper, practical applicability is limited when dealing with exceptional behavior and processes that cannot be described as a structured workflow net without short loops. This paper presents the Alpha+++ algorithm that overcomes many of these limitations, making the algorithm competitive with more recent process mining approaches. The different steps provide insights into the practical challenges of learning process models with concurrency, choices, sequences, loops, and skipping from event data. The approach was implemented in ProM and tested on various publicly available, real-life event logs.