Experimental characterization of strong, anisotropic H-2 hyperfine interactions in randomly oriented organic radicals in the solid state by using electron spin echo envelope modulation (ESEEM) spectroscopic techniques has been examined systematically. The alpha-3,5-H-2 coupling in the tyrosine neutral radical in a low temperature aqueous glass was used as a model. Envelope modulation was obtained by integration of the stimulated-echo generated by a three-pulse, microwave pulse-swapping sequence. Division of envelope modulation from the H-2-substituted radical by that from the per-protonated radical remedies discontinuities introduced in the envelope by the eclipse of the second and third pulses. Envelope modulation data was collected for tau values from 214 to 1295 ns. (9.132 GHz, 0.3265 T). The common, spectrometer dead-time-limited data collection start-point (140 ns) for the different tau values attenuates loss of anisotropic information and allows summation of time domain data. The Fourier transform of the envelope summation shows the line shape determined only by the orientation-dependencies of the modulation depth and the random distribution of spin systems. The systematic influence of tau-suppression on the line shapes is examined in the individual spectra. Intensity in the region of the Delta m(1) = +/- 2, double quantum transition is revealed at values of tau sufficiently long to relieve tau-suppression of this feature. Algebraic expressions for the orientation-dependence of the modulation frequencies and amplitudes are given for the;general case of rhombic hyperfine interaction in S = 1/2, I = 1 systems where hyperfine interactions dominate nuclear quadrupole coupling, and are used to describe the changes in the experimental line shapes wrought by variation of tau and magnetic held strength. Theoretical simulation of the spectra yields the complete 3,5-H-2 hyperfine tenser, (-3.0, -3.9, -1.1) +/- 0.1 MHz. The results show that the sculpting of the ESEEM line shape by the suppression effect allows retrieval of information, obscured by the orientation dependence of the modulation depth, that is necessary to determine the rhombic hyperfine tenser.