  We consider deletion correcting codes over a q-ary alphabet. It is well known
that any code capable of correcting s deletions can also correct any
combination of s total insertions and deletions. To obtain asymptotic upper
bounds on code size, we apply a packing argument to channels that perform
different mixtures of insertions and deletions. Even though the set of codes is
identical for all of these channels, the bounds that we obtain vary. Prior to
this work, only the bounds corresponding to the all insertion case and the all
deletion case were known. We recover these as special cases. The bound from the
all deletion case, due to Levenshtein, has been the best known for more than
forty five years. Our generalized bound is better than Levenshtein's bound
whenever the number of deletions to be corrected is larger than the alphabet
size.
