Tier 1 income taxable to the beneficiaries includes income required to be distributed even if it is not distributed before the end of the estate's income tax year. The requirement to distribute is a matter of state law and the terms of the will. However, even if the income is permitted to remain in the estate and be taxed in the estate, except for small amounts of income it seems that it would not be in the beneficiaries' interests to have the income taxed at estate tax rates because estate income tax rate is likely to be higher than that of the beneficiaries.
I suggest reviewing IRS Pub 559 and the instructions for Form 1041.
