| align="left" | "Money Burns a Hole in My Pocket" (B-side of "Sway") | 23 | — | — | — | rowspan="2" align="center" |Living It Up (EP rel. 6/7/54) |- | align="left" | "How Do You Speak to an Angel" | — | — | 15 | — |- | align="left" | "That's What I Like" | — | 29 | — | — | rowspan="4" align="center" | — |- | align="left" | "The Peddler Man" (B-side of "That's What I Like") | — | 33 | — | — |- | align="left" | "Try Again" | — | 36 | — | — |- | align="left" | "One More Time" (B-side of "Try Again") | — | 44 | — | — |- | rowspan="10" | 1955 | align="left" | "The Naughty Lady of Shady Lane" (UK & AU Single only) | — | — | 5 | 1 | rowspan="4" align="center" |Dean Martin (EP rel. December 13, 1954) |- | align="left" | "Mambo Italiano" (UK & AU Single only) | — | — | 14 | 2 |- | align="left" | "Let Me Go Lover" (UK & AU Single only) | — | — | 3 | 1 |- | align="left" | "That's All I Want from You" (UK & AU Single only) | — | — | — | 4 |- | align="left" | "Young and Foolish" | — | 34 | 20 | — | rowspan="4" align="center" | — |- | align="left" | "Under the Bridges of Paris" (B-side of "Young and Foolish") | — | — | 6 | — |- | align="left" | "Open Up the Doghouse" (with Nat King Cole) | — | 22 | — | 19 |- | align="left" | "Chee Chee-Oo Chee (Sang The Little Bird)" | — | — | — | 8 |- | align="left" | "Memories Are Made of This" | 1 | 1 | 1 | 1 | rowspan="1" align="center" |Memories Are Made of This (EP rel. December 12, 1955) & Hey, Brother, Pour the Wine |- | align="left" | "Relax-ay-Voo" | — | — | — | 16 | rowspan="1" align="center" |Single only |- | rowspan="8" | 1956 | align="left" | "Innamorata" | 27 | 17 | 21 | 20 | rowspan="1" align="center" |Artists and Models (EP rel. December 26, 1955) |- | align="left" | "Standing on the Corner" | 22 | — |