Samples used in Doppler-effect measurements in fast critical assemblies distort the flux in their vicinity. For fissile samples whose Doppler effect depends strongly on spectrum, this distortion may strongly affect the measured results. An integral transport method for computing distorted real and adjoint fluxes is developed and the fissile-sample Doppler measurements in a fast critical assembly, ZPR-6 Assembly 7, are analyzed. It was found that the local flux distortions strongly affect the results and for a PuO2 sample even change the algebraic sign of the Doppler effect.