The y-decay of levels in 2aNe up to 10 MeV excitation energy has been investigated by n-y coincidence measurements initiated with the 180(a, ny) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining the n-y angular correlation measurements performed at E~ = 11, 11.82 and 13.6 MeV with a consideration of lifetimes, ne~atron penetrabilities of the unbound states, and information from the mirror nucleus 21Na. The resulting values of Ex[keV]-2J ~ are as follows: 4525-5 +, 4686-3 +, 5431-7 +, 5549-3 +, 5819-7-, 6175-7 +, 6268-9 +, 6550-9, 6639-9, 7006-7 +, 7041-9, 7356-7 or 9, 7422-11 (-t, 7648-7 +, 7981-11 or (7+), 8154-9, 8240-11, 8664-9-or 11 or 13-, 9401-13-, 9867-13-or 15 +, 9941-13-or 15 or 17 +. The assignment of mirror levels in 21Ne -2~Na has been extended to the 6175 keV level of 2aNe. Excitation energies, electromagnetic properties, Gamow-Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unified s-d shell Hamiltonian and the unrestricted configuration space of the 0d5/2 -1 s~/2-Od3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands at J= 17/2 or 19/2. The spectrum of intruder states in 2~Ne is observed to begin with a 5628 keV, J~=7/2 + state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.