We construct microscopic models of compacting sediment which lead to inclination shallowing of the magnetic remanence. The models can be classified as (1) rotation of elongated magnetic grains to more horizontal orientations; (2) rotation toward the horizontal of flat nonmagnetic fabric grains to which smaller magnetic grains are attached; (3) randomization of the sediment by grain rotations which lead to decreased intensity of magnetization and possibly also to inclination shallowing; and (4) finally, we show that the initial within-sample dispersion of the magnetic moments dampens the amount of inclination shallowing of all the models and transforms any form of microscopic mechanism to an equation of standardized form. The physically realistic models rise to different magnitudes of inclination shallowing, which to the first order obey an equation of the form tan (I-ΔI)=(1-a ΔV) tan I, where K is the inclination of the ambient field, ΔI is the inclination shallowing and ΔV the compaction. For these models we also calculate the effect of compaction on the intensity of magnetization, and the results show that considerable randomization is needed to offset the increased intensity due to higher concentrations of magnetic particles caused by compaction. If random rotation of the grains are biased toward rolling about horizontal axes and the randomization is sufficient to cancel the effect of greater concentrations, then the random grain rolling due to the compaction would give rise to considerable inclination shallowing. ¿ American Geophysical Union 1990