  Alon and F\"{u}redi (1993) showed that the number of hyperplanes required to
cover $\{0,1\}^n\setminus \{0\}$ without covering $0$ is $n$. We initiate the
study of such exact hyperplane covers of the hypercube for other subsets of the
hypercube. In particular, we provide exact solutions for covering $\{0,1\}^n$
while missing up to four points and give asymptotic bounds in the general case.
Several interesting questions are left open.
