Wolf, the idea is that something that is Huktza Lemitzvassa belongs entirely to the Mitzva, it is more a Chefetz Shel Mitzva than something that is used for a Mitzva but remains yours for the usage all along.
deiyazooger, Where did you see/hear that a T’nai would help? It seems from the Beis Yosef and the Bach that the problem is even if it burned more than a half hour every night, because the rest is mixed in with it.