The pulsed neutron problem is studied in small but finite sized assemblies of liquid water and heavy water poisoned with such non-1/v neutron absorbers as samarium, cadmium, and gadolinium. It is found that the asymptotic neutron density is markedly dependent on the nature of the non-1/v absorber. For a given buckling, one can find a critical concentration of gadolinium that will give a Maxwellian asymptotic neutron distribution. Thus, a finite assembly in the presence of a definite concentration of gadolinium acts as an infinite assembly. This is not the case with samarium or cadmium.