Irving Berlin wrote "Be Careful, It's My Heart" for the Bing Crosby - Fred Astaire musical Holiday Inn. Bing's performance in the movie isn't available on YouTube but here's a recording he made in 1942. Sinatra's recording about two decades later doesn't seem to have been influenced by Bing's zing-less, ring-a-ding-ding-less version at all:
I love the way Frank sings "remembuh" and tosses off "it's my heart," breezily yet pointedly. But I have to admit, the way he finishes on that high note has not grown on me over the years. This is the one song on Ring-a-Ding Ding! that Johnny Mandel had no part in arranging. He was pressed for time and had Skip Martin ghost-arrange it. From Frank Jr.'s liner notes:
This orchestration, actually written by Skip Martin of MGM fame, finishes with Sinatra hitting a double "F." Martin says, "When I first heard the playback, I asked him 'Why did you reach for that high ending?' He smiled at me and said, 'There was nowhere else I could go.'"Oh, well. Nobody's perfect. I still like it enough to rank it in my top forty.