Excused Absences: Increase the numerator, lower the denominator, or...?

I have a simple attendance grading item. Suppose we have 20 possible lectures. A typical student would get a score of recorded attendance/20. What if they get an excused absence? There are many options:

1. Give them the missing point, so instead of say 15/20, they would get 16/20. I dislike this option because it seems wrong to give credit for something that was missed entirely. I rather favor option 2, which is:
2. Reduce the denominator by 1, so they now have 15/19. The two options (1) and (2) are not equivalent, since 16/20 is 80% of the points while 15/19 is 78.9%. Although that isn't much, if many classes are missed the difference between (1) and (2) becomes larger.
3. Give a 'grace absence' of, say, two, so you're counting everyone out of 18 with a maximum of 18. I dislike this one since students will provide you medical notes so that they can exceed the two, as in "I don't want my medical absence to count as one of the free ones" and I would have to contend with the same issue anyways.
4. Provide a way to make up the missing point. I dislike this one because it's work for me, and if we start doing this, then more students will want it. By the end of term I'll have 50% attendance and bunch of extra stuff to grade.
5. Add the missing points to an exam. I dislike this one because it makes their exam count for a greater percentage of their score, plus in theory a student could replace all attendance this way. There should be an incentive to come to class.

What do you all do for excused absences?

Edit: For clarification, I give an in-class worksheet and grade for participation (credit). It is a de facto attendance grade.