Energy levels and radiative rates for electric dipole (E1) transitions among the lowest 141 levels of the (1s 22s 22p 6) 3ℓ 2, 3ℓ3ℓ', and 3ℓ4ℓ configurations of Fe XV, Co XVI, and Ni XVII are calculated through the CIV3 code using extensive configuration-interaction (CI) wavefunctions. The important relativistic effects are included through the Breit-Pauli approximation. In order to keep the calculated energy splittings close to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. The energy levels, including their orderings, are in excellent agreement with the available experimental results for all three ions. However, experimental energies are only available for a few levels. Since mixing among some levels is found to be very strong, it becomes difficult to identify these uniquely. Additionally, some discrepancies with other theoretical work (particularly for Ni XVII) are very large. Therefore, in order to confirm the level ordering as well as to assess the accuracy of energy levels and radiative rates, we have performed two other independent calculations using the GRASP and FAC codes. These codes are fully relativistic, but the CI in the calculations is limited to the basic (minimum) configurations only. This enables us to assess the importance of including elaborate CI for moderately charged ions. Additionally, we report results for electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions, and list lifetimes for all levels. Comparisons are made with other available experimental and theoretical results, and the accuracy of the present results is assessed.