  One peculiarity with deletion-correcting codes is that perfect
$t$-deletion-correcting codes of the same length over the same alphabet can
have different numbers of codewords, because the balls of radius $t$ with
respect to the Levenshte\u{\i}n distance may be of different sizes. There is
interest, therefore, in determining all possible sizes of a perfect
$t$-deletion-correcting code, given the length $n$ and the alphabet size~$q$.
In this paper, we determine completely the spectrum of possible sizes for
perfect $q$-ary 1-deletion-correcting codes of length three for all $q$, and
perfect $q$-ary 2-deletion-correcting codes of length four for almost all $q$,
leaving only a small finite number of cases in doubt.
