In this article the problem of bounding transient growth in iterative learning control (ILC) is examined. While transient growth is not a desirable property, the alternative, robust monotonic convergence, leads to fundamental performance limitations. To circumvent these limitations, this article considers the possibility that some transient growth, if properly limited, is a viable and practical option. Towards this end, this article proposes tools for analysing worst-case transient growth in ILC. The proposed tools are based on pseudospectra analysis, which is extended to apply to ILC of uncertain systems. Two practical problems in norm-optimal ILC weighting parameter design are considered. Using the presented tools, it is demonstrated that successful design in the transient growth regime is possible, i.e. the transient growth is kept small while significantly improving asymptotic performance, despite model uncertainty.