Alternatives to dropping a test

I teach chemistry at a medium-sized, public liberal arts institution with small class sizes. I have decided not to drop exam scores because I hate to give students the impression that they only need to learn 2/3 of the material (or 4/5 or 3/4, etc). This is particularly a bad idea for subjects that are so cumulative. Instead, I may make their worst test worth only 10%, when the remainder are worth 20% of their final grade. They are still penalized for a poor performance on an exam, but it gives them a chance to rescue their score if they apply themselves. I do not let students make up exams, either. If they miss an exam for illness, death in the family, fill-in-the-blank, then I assign a score to the missed test-- the average of their remaining tests. Since poor students will often invent excuses to miss an exam in fear of doing poorly again, this gives them no real advantage. The average of their previous and future poor scores will substitute for the missed score. I have a statement in the syllabus that only one exam can be missed for any reason. Another colleague of mine allows students to miss exams, but adds the weight of that exam onto the weight of the final exam. So, if there are 5 tests worth 15% and a final worth 25%, a student who misses an exam for any reason now has a final exam that is worth 40%. It makes a student with the sniffles evaluate how sick they really are. A student that hands in an assignment late can only receive as a maximum the lowest score of student work that was handed in on time. So if Suzy turned in her work on time but only got a 60 out of 100 points, then Joey who turned his assignment in late can only get 60 points, even if the assignment is perfect. I have found these policies to minimize excuses because there are options open to them, but usually the skipping/late option is worse.