We report on numerical simulations of the electron addition spectra in quantum dots weakly coupled to one charge reservoir, and containing a small number (N ≤ 10) of particles. In particular, we investigate the role played by disorder and electron-electron interaction in creating a surprising feature, known as “electron bunching”, recently observed experimentally. In dots where disorder and on-site repulsion are both strong, and the direct Coulomb repulsion is short range, we find examples of two electrons entering the dot at very close values of the gate voltage. Whenever such pairing occurs, the first electron involved in the pair appears at the edge of the quantum dot. Furthermore, the tunneling rate of the second electron is much faster than that of the first. We also find that the total spin of the many-body ground state is partially polarized after the second electron enters the dot. The dependence of the addition spectrum as a function of the magnetic field is discussed.