Particle y-ray coincidences have been measured in the 28Si (d, py) reaction at 6.5 and 7 MeV bombarding energy, in the 26Mg (c~, ny) reaction at 12, 14 and 15 MeV, and in the 27A1 (z, py) reaction at 9 MeV. The ;~-decay has been observed for all bound states of 29Si and for 56 unbound states up to 12,960 KeV excitation energy. Particle ?;-ray angular correlations were measured in the 2ssi (d, pT) reaction at 6.5 MeV and in the 26Mg (cg nT) reaction at 12 MeV. Spin (-parity) assignments or restrictions were obtained for nearly all bound states and some high-spin states above the binding energy. The assignment of mirror levels in 29Si and 29p has been extended to 8.2 MeV excitation energy. The excitation energies of 41 positive-parity states are reproduced by shell model calculations. The possible existence of a K~=5/2 + band with prolate deformation is discussed.