Stormwater drainage and other water systems are vulnerable to changes in rainfall and runoff and need to be adapted to climate change. This paper studies impacts of rainfall variability and changing return periods of rainfall extremes on cost-effective adaptation of water systems to climate change given a predefined system performance target, for example a flood risk standard. Rainfall variability causes system performance estimates to be volatile. These estimates may be used to recurrently evaluate system performance. This paper presents a model for this setting, and develops a solution method to identify cost-effective investments in stormwater drainage adaptations. Runoff and water levels are simulated with rainfall from stationary rainfall distributions, and time series of annual rainfall maxima are simulated for a climate scenario. Cost-effective investment strategies are determined by dynamic programming. The method is applied to study the choice of volume for a storage basin in a Dutch polder. We find that 'white noise', i.e. trend-free variability of rainfall, might cause earlier re-investment than expected under projected changes in rainfall. The risk of early re-investment may be reduced by increasing initial investment. This can be cost-effective if the investment involves fixed costs. Increasing initial investments, therefore, not only increases water system robustness to structural changes in rainfall, but could also offer insurance against additional costs that would occur if system performance is underestimated and re-investment becomes inevitable.