We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insight obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines that point towards the two-particle Stark saddle in the presence of a field. The resulting effective two-dimensional model is similar to the aligned electron model, but it enables correlated escape of electrons with equal momenta, as observed experimentally. The time-dependent solution of the Schrödinger equation allows us to discuss in detail the time dynamics of the ionization process, the formation of electronic wave packets, and the development of the momentum distribution of the outgoing electrons. In particular, we are able to identify the rescattering process, simultaneous direct double ionization during the same field cycle, as well as other double ionization processes. We also use the model to study the phase dependence of the ionization process.