Thermonuclear plasmas with a sufficient density-radius product, ρR, will degrade the energy spectrum of neutrons released in the plasma. This property may alleviate neutron damage, transmutation, and transient power loading in the first wall of laser-controlled thermonuclear reactors. In addition, degraded neutron energy spectra might be used as a diagnostic of compression in latter-stage laser fusion experiments. As an example of the degradation in the neutron spectrum, the energy spectrum of neutrons resulting from a thermonuclear deuterium-tritium plasma with ρR = 2 g/cm2 when using a simple model shows that ∼2.5 MeV of the neutron’s original 14.1 MeV is deposited in the pellet. As a figure of merit for the reduction of threshold reactions in the walls, the same model shows that ∼27%> of the neutrons are below 10 MeV in energy.