We present highly resolved photoluminescence studies on heat-treated nominally undoped InP, which was either unprotected or protected by SiO2 or Si3N4 caps during the annealing procedures. Annealing of InP above 350°C leads to six different sharp emissions in the wavelength range between 8790 and 8900 Å, which are not observed at 4 K in Zn-doped or Fe-doped samples. Based on temperature-dependent photoluminescence studies, time-resolved measurements and preliminary magnetic field studies we ascribe these emissions to isoelectronic bound exciton transitions. It is also shown that the two emissions at 8883 Å (11254 cm-1) (E) and 8889 Å (11246 cm-1) (F) belong to one center. We observe that the lines not only depend on the heat treatment but also on some unintentionally incorporated or residual impurities of a low concentration level. Possible candidates are discussed.