We have measured the intensity of anhysteretic remanent magnetization (ARM) as a function of alternating field (AF) decay rate. For synthetic and natural single-domain (SD) and pseudo-single-domain (PSD) magnetites, ARM intensity increases as decay rate decreases. Multidomain (MD) magnetites have the opposite response, ARM increasing as the decay rate increases. These are identical to the SD/PSD and MD dependences of thermoremanent magnetization on cooling rate. For all grain sizes and domain structures, ARM intensity increases as the AF decay rate used to achieve an initial demagnetized state decreases. Decay-rate differences in ARM intensity are a property of low- and medium-coercivity grains, as shown by annealing and by stepwise AF demagnetizing samples. We interpret the SD results to mean that increased AF exposure time permits a closer approach to equilibrium magnetization. An approximate thermal activation theory based on N¿el <1949> and an exact theory by Egli and Lowrie <2002> predict 6--11% increases in ARM for an order of magnitude decrease in decay rate, in reasonable accord with the observed 12% increase for 0.065 ¿m SD grains. For MD grains, we hypothesize that increased exposure time (slower decay) permits more efficient self-demagnetization, reducing ARM. Low-coercivity grains experience the largest self-demagnetizing fields and therefore have the largest decay-rate response. Initial-state decay-rate response is attributed to longer exposure times leaving domain walls more strongly pinned in deeper potential wells (the net self-demagnetizing field is zero in the demagnetized state). Acquisition decay-rate, annealing, and initial-state responses of PSD grains are a blend of SD and MD responses. Because ARM is the most frequently used normalizer in relative paleointensity determination, it is important either to use a standard decay rate or else to remove the decay-rate dependence by demagnetizing the ARM to ~30% of its initial value (ARM0.3). A standard demagnetization level for the normalizing ARM is particularly important when comparing paleointensity records from different laboratories.