Crazy bartender's pithy way to commemorate initial delivery (8,7)

I believe the answer is:

birthday present

I'm a little stuck... Click here to teach me more about this clue!

'commemorate initial delivery' is the definition.
I can't judge whether this defines the answer.

'crazy bartender's pithy way' is the wordplay.
'crazy' is an anagram indicator.
'way' becomes 's' (Compass direction - South).
'bartender'+'pithy'+'s'='bartenderpithys'
'bartenderpithys' anagrammed gives 'BIRTHDAY PRESENT'.

'to' acts as a link.

Can you help me to learn more?

(Another definition for birthday present that I've seen is " gift".)

I've seen this clue in The Irish Times.

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