It IS possible for a surviving veteran to receive Dependency and Indemnity Compensation (DIC) Benefits from the Department of Veterans Affairs (VA) based on the deceased spouse’s military service as well as a VA Pension Benefit based on the survivor’s own military service, but any DIC award based on the deceased spouse’s service will be considered as countable income in calculating the Pension Benefit payable to the surviving veteran. Unfortunately, however, the applicable regulations are a bit contradictory:

§ 3.700. General.
Not more than one award of pension, compensation, or emergency officers’, regular or reserve retirement pay will be made concurrently to any person based on his or her own service except as provided in § 3.803 relating to naval pension and § 3.750(c) relating to waiver of retirement pay.
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(4) Improved pension. If a veteran is entitled to improved pension on the basis of the veteran’s own service and is also entitled to pension under any pension program currently or previously in effect on the basis of any other person’s service, the Department of Veterans Affairs shall pay the veteran only the greater benefit.
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(b) Dependents- (1) Surviving spouse. Subject to the provisions of paragraph (a)(4) of this section, the receipt of pension, compensation, or dependency and indemnity compensation by a surviving spouse because of the death of any veteran, or receipt of pension or compensation because of his or her own service, shall not bar the payment to the surviving spouse of pension, compensation, or dependency and indemnity compensation because of the death or disability of any other veteran; however, other than insurance, concurrent benefits under laws administered by the Department of Veterans Affairs may not be authorized to a surviving spouse by reason of the death of more than one veteran to whom the surviving spouse has been married. The surviving spouse may elect to receive benefits based on the death of one such spouse and the election places the right to benefits based on the deaths of other spouses in suspense. The suspension may be lifted at any time by another election based on the death of another spouse. Benefits payable in the elected case will be subject to prior payments for the same period based on the death of the other spouse where, under the provisions of § 3.400(c), there is entitlement in the elected case prior to date of receipt of the election.