I used to write wills for a living and (apart from the need to expand the date to read 'this eleventh day of December in the year two thousand and eleven', and to include the full address of John Smith) I'm confident that PP's draft would suffice.
However I'd prefer to see a specific reference included to state what should happen if the intended beneficiary was to die before you (or, for example, to die in the same road accident). So, after 'absolutely', I'd add something like 'subject to the proviso that the said John Smith shall survive me for a period of thirty days. If John Smith does not survive me for such period . . . [as required]'.
Chris