Applications of long-wavelength (lambda > 1 mu m) vertical-cavity surface-emitting lasers (VCSELs) generally require close control over wavelength and polarization of the emitted light. In most cases, single mode and polarization stable lasing is desired. We report here on the detailed modal analysis of wafer-fused 1550-nm wavelength VCSELs incorporating an AlGaInAs/InP active region, a re-grown circular tunnel junction (TJ) and undoped AlGaAs/GaAs distributed Bragg reflectors (DBRs). We experimentally determined the diameter of the TJ that optimizes the output power and threshold current, finding a value between 7.0 mu m and 9.5 mu m depending on the temperature. Moreover, we investigated the impact of the TJ aperture diameter on the mode structure. A large batch of devices was investigated, allowing drawing conclusions on typical behavior of these devices.