The unimolecular dissociation of the C3H4 isomers allene and propyne has been examined using two complementary shock-tube techniques : laser schlieren (LS) and time-of-flight (TOF) mass spectrometry. The LS experiments cover 1800-2500 K and 70-650 Torr, in 1, 2, and 4% propyne/Kr and 1 and 2% allene/Kr, whereas the TOF results extend from 1770 and 2081 K in 3% allene or propyne in Ne. The possible channels for unimolecular dissociation in the C3H4 system of isomers are considered in detail, using new density functional theory calculations of the barriers for insertion of several C3H2 into H-2 to evaluate the possibility of Hz elimination as a dissociation route. The dominant path clearly remains CH fission, from either isomer, as suggested in earlier work, although some small amount of H-2 elimination may be possible from allene. Rate constants for the CH fission of both allene and propyne were obtained by the usual model-assisted extrapolation of LS profiles to zero time using an extensive mechanism constructed to be consistent with both the time variation of LS gradients and the TOF product profiles. This procedure then provides rate constants effectively independent of both the near-thermoneutral isomerization of the allene/propyne and of secondary chain reactions. Derived rate constants show a strong, persistent pressure dependence, i.e., a quite unexpected deviation (falloff) from second-order behavior. These rate constants are nearer first than second order even for T > 2000 K. They are also anomalously large; RRKM rates using literature barriers and routine energy-transfer parameters are almost an order of magnitude too slow. The two isomers show slightly differing rates, and falloff is slightly less in allene. It is suggested that isomerization is probably slow enough for this difference to be real. The anomalously large rates and falloff are both consistent with an unusually large low-pressure-limit rate in this system. Extensive isomerization of these C3H4 is possible for energies well below their CH fission barriers, and this can become hindered internal rotation in the activated molecule. On the C3H4 surface we identify three such accessible rotors. State densities for the molecule including these rotors are calculated using a previous general classical formulation. Insertion of these state densities into the RRKM model results in rates quite close to the measured magnitudes, and showing much of the observed falloff. The increase in the low-pressure rate is as much as a factor of 8; a necessary but nonetheless remarkable effect of anharmonicity on the unimolecular rate. This again demonstrates the importance of accessible isomerization and consequent hindered internal rotation on the rate of dissociation of unsaturated species.