The recently introduced models of reionization bubbles based on extended Press–Schechter theory (by Furlanetto, Hernquist & Zaldarriaga) are generalized to include mergers of ionization sources. Sources with a recent major merger are taken to have enhanced photon production due to star formation, and accretion on to a central black hole if a black hole is present. This produces a scatter in the number of ionized photons corresponding to a halo of a given mass and a change in photon production over time for any given halo mass. By extending previous methods, photon production histories, bubble distributions and ionization histories are computed for several different parameter and recombination assumptions. The resulting distributions interpolate between previously calculated limiting cases.