From the abstract at Health Physics Journal:

"The 131-I thyroid absorbed dose is two-fold greater with insufficient levels of dietary iodine, 2,900 cGy/37 MBq, than with sufficient levels of dietary iodine, 1,500 cGy/37 MBq. When KI is administered 48 h or less before 131-I intake, the thyroid absorbed doses (in cGy/37 MBq) are comparably low with both sufficient and insufficient dietary iodine levels. When KI is administered after 131-I intake, however, the protective effect of KI is less and decreases more rapidly with insufficient than with sufficient dietary iodine. For example, KI administration 2 and 8 h after 131-I intake yields protective effects of 80 and 40%, respectively, with iodine-sufficient diets, but only 65 and 15% with iodine-deficient diets."