Here we develop a new control model of water injection from a growing hydrofracture into a layered soft rock. We demonstrate that in transient flow, the optimal injection pressure depends not only on the instantaneous measurements, but also on the whole history of injection, growth of the hydrofracture, and the rock damage. Based on the new model, we design an optimal injection controller that manages the rate of water injection in accordance with hydrofracture growth and the formation properties. We conclude that maintaining the rate of water injection into a lowpermeability rock above a reasonable minimum inevitably leads to hydrofracture growth, to establishment of steady-state flow between injectors and neighboring producers, or to a mixture of both. Analysis of field water injection rates and wellhead pressures leads us to believe that direct links between injectors and producers can be established at early stages of waterflood, especially if the injection policy is aggressive. Such links may develop in thin, highly permeable reservoir layers or may result from failure of the soft rock under stress exerted by injected water. These links may conduct a substantial part of injected water. Based on the field observations, we now consider a vertical hydrofracture in contact with a multilayer reservoir, where some layers have high permeability and quickly establish steady-state flow from an injector to neighboring producers.