Composer Jule Styne and lyricist Sammy Cahn wrote “I Fall in Love Too Easily” for the 1945 film Anchors Aweigh which was a big success for the MGM studio. Co-star Frank Sinatra, who had enjoyed several hits with Styne/Cahn songs, requested that they write the songs for the film in which he introduced the Oscar-nominated song “I Fall in Love Too Easily.” The picture won the Oscar for Best Music and Scoring of a Musical Picture (George E. Stoll). (The movie title is also the title of the song of the United States Navy, composed in 1906 by Charles A. Zimmerman with lyrics by Alfred Hart Miles.)
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Википедия
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There are those who can leave love or take it
Love to them is just what they make it
I wish that I were the same
But love is my fav'rite game

I fall in love too easily
I fall in love too fast
I fall in love too terribly hard
For love to ever last

My heart should be well-schooled
'Cause I've been burned in the past
And still I fall in love too easily
I fall in love too fast

I fall in love too easily
I fall in love too fast
I fall in love too terribly hard
For love to ever last