The active ingredient in most over-the-counter sleep aids is
Diphenhydramine HCl (aka Benedryl). For many brands, the standard dose
is 50 mg, but Tylenol's Simply Sleep contains just 25mg per caplet.
You might want to try that product, or try taking a smaller dose (1/2
or 1/4 tablet) of whatever brand you happen to buy. You may be less
likely to experience prolonged drowsiness that way.

BTW, I've found that generic diphenhydramine (in the allergy section)
is usually the cheapest option.

Richard, over the counter options to sleeping problems is not
advisable since it tends to, like mentioned, have bad side effects
like "hang-over" effect the next day.  Also one tends to develop
tolerance to these agents so that you are just left with side-effects
rather than relief.  Sleeping problems are mostly attributed to
stress.  An Valerian root or Rescue Remedy alternative would most
probably be an better option (e.g Calmettes, Restin) since it is more
natural.  If the problems persists, it most probably need to be
attended to by professional like general practioner in order to
prescribe something that will get you in a sleeping pattern.  Of
course there is always the usual advise like: trying not to exercise
too late, not drinking caffeine containing beverages before going to
bed,  quite sleeping evironment, etc.