Based on German hourly feed-in and consumption data for electric power, this paper studies the storage and buffering needs resulting from the volatility of wind and solar energy. It shows that joint buffers for wind and solar energy require less storage capacity than would be necessary to buffer wind or solar energy alone. The storage requirement of over 6,000 pumped storage plants, which is 183 times Germany’s current capacity, would nevertheless be huge. Taking the volatility of demand into account would further increase storage needs, and managing demand by way of peak-load pricing would only marginally reduce the storage capacity required. Thus, only a buffering strategy based on dual structures, i.e. conventional energy filling the gaps left in windless and dark periods, seems feasible. Green and fossil plants would then be complements, rather than substitutes, contrary to widespread assumptions. Unfortunately, however, this buffering strategy loses its effectiveness when wind and solar production overshoots electricity demand, which happens beyond coverage of about a third of aggregate electricity production. Voluminous, costly and inefficient storage devices will then be unavoidable. This will make it difficult for Germany to pursue its energy revolution beyond merely replacing nuclear fuel towards a territory where it can also crowd out fossil fuel.