The Fe54(t,p)Fe56 reaction was studied with 12-MeV incident tritons using the Aldermaston tandem Van de Graaff and multigap spectrograph. The angular distributions of the protons are characterized by sharp structure. For eight cases where the spin and parity of the final state are known, the position of the first maximum agrees very well with predictions of the plane-wave Born approximation. These positions were then used for assigning spins and parities to many other levels. The only known unnatural parity state is excited two orders of magnitude less strongly than the strongly excited states, and has an unusual angular distribution. The collective 3- state (4.51 MeV) is the most strongly excited state in the spectrum; it is shown that this is very difficult to explain. Other very strongly excited states are the ground and first excited states, 1- states at 5.19 and 7.06 MeV, and a 6+ (or 7-) state at 5.15 MeV. The spin and parity assignments of all states up to 4.5 MeV are discussed in the light of other evidence; the principal correction is to change the assignment of the 3.122-MeV state from 5+ to 5-.