A11 controller described operational error event when departure was assigned routing that violated MVA standards.

Narrative

I was working the south radar position at Anchorage TRACON (A11). I was given C208 off Runway 7L filed direct ENA (Kenai) at 4;000 FT. I called the C208 radar contact and put the aircraft direct ENA as per our LOA with ZAN. I received a departure roll strip on a DH8A (also departing Runway 7L) that was also filed direct ENA at 4;000 FT. The strip indicated that the DH8A was given a 10 DME restriction; meaning the aircraft was to proceed runway heading to 10 DME before they started their turn to the south to a heading of 200 degrees. When the DH8A was airborne at 1;700 FT; I called the Anchorage Tower and instructed them to stop the DH8A at 2;000 FT and turn him direct ENA. The Controller informed me that he had already switched the plane to my frequency. When the DH8A pilot checked in at 2;100 FT with me; I radar-identified the aircraft and issued a climb to 3;000 FT and turned them direct ENA. The A11 and ZAN LOA say; 'that we can only go direct ENA at 2;000 FT; 4;000 FT; or at or above 6;000 FT.' I asked the DH8A Pilot if they could accept 2;000 FT enroute to ENA. The pilot answered in the affirmative. The aircraft at this time was climbing out of 2;500 FT in a 2;500 FT MVA direct ENA. I descended the aircraft to 2;000 FT.