Thanks to nonparametric estimators coming from machine learning, microlevel reserving has become more and more popular for actuaries. Recent research focused on how to integrate the whole information one can have on claims to predict individual reserves, with varying success due to incomplete observations. Using the CART algorithm, we develop new results that allow us to deal with large reporting delays and partially observed explanatory variables. Statistically speaking, we extend CART to take into account truncation of the data, and introduce plug-in estimators. Our applications are based on real-life insurance portfolios embedding Income Protection and Third-Party Liability guarantees. The full knowledge of the claim lifetime is shown to be crucial to predict the individual reserves efficiently.