Boy, this reader knows his Sinatra.

Dear Mr. Derbyshire—Right on Sinatra. It seems likely that Frank overall
choose not to do verses when they were of lesser quality, when they sounded
too much intended for a woman (as with ‘It Never Entered My Mind’) or if,
when dealing with an uptempo chorus — such as on ‘Love is Here to Stay’ or
’Pennies from Heaven’ — they would bog things down. Still, I would have
liked to have heard the verse on such as ‘All the Things You Are.’
But verses he did include (as I can remember them):
Ol’ Man River: 1944 and 1963.
When Your Lover Has Gone: 1944 and 1954.
Over the Rainbow: 1945 (and not even Judy did that one).
Try a Little Tenderness: 1945 version.
Five Minutes More: 1946 version.
September Song: 1961 and 1965 versions, with the ‘65 version the full verse.
Guess I’ll Hang My Tears Out to Dry: 1946 and 1958 versions.
Tea for Two: 1947.
Fools Rush In: 1947 (not ‘60 version).
I’ve Got a Crush on You: 1947, 1960 and 1966 versions.
Don’t Cry Joe: 1949 version.
The Birth of the Blues: 1952.
(Don’t Worry ‘Bout Me: probably recorded it for the 1953 version and then
cut it off — that’s why it opens so abruptly).
A Foggy Day: 1953 version.
They Can’t Take That Away from Me: 1953 — well, a verse, just not the
Gershwin’s.
Violets for Your Furs: 1953.
I Get a Kick out of You: 1953 and 1974 versions.
Little Girl Blue: 1953.
The Girl Next Door: 1953 and 1962.
Can’t We Be Friends?: 1954.
Glad to Be Unhappy: 1954.
P.S. I Love You: 1956.
Blame it on My Youth: 1956.
Everything Happens to Me: 1956 version.
Lonely Town: 1957.
Angel Eyes: 1958 and 1966.
Dancing in the Dark: 1958 — no verse, but it has a 16-bar “trio” in the
middle, which Sinatra does.
I Can’t Get Started: 1959 (new lyrics added with old).
Let’s Fall in Love: 1960.
Have You Met Miss Jones?: 1960 version, not released (verse arrangement had
mistakes in it).
Zing Went the Strings of My Heart: 1960 (only released 30 years later).
Stardust: 1961 (just verse).
Night and Day: 1961.
Roses of Picardy: 1962.
My Heart Stood Still: 1963.
Bewitched: 1963.
Talk to Me Baby: 1963.
The Man in the Looking Glass: 1965.
It Gets Lonely Early: 1965 (verse recorded but dropped because of
difficulty, prompting Sinatra to sing “it gets lousy early”).
Moon Song: 1965.
I Wished on the Moon: 1965.
Dindi: 1967.
It Had to Be You: 1979.
My Shining Hour: 1979.
More Than You Know: 1979.
But Not for Me: 1979.

[Derb here] I note, by the way, from Mia Farrow’s memoirs, that Sinatra,

just like the rest of us, put on a Sinatra record for purposes of seduction.