Fleisher is renowned for his mastery of piano works for one hand. In the 1960s, when a neurological ailment prevented him from using his right hand, he played solely with his left.

Periodic attempt to return to the standard, two-handed repertoire failed until recent treatments of Botox returned the use of the pianist's right hand. Fleisher's recent album Two Hands, which went as high as the number-two position on the Billboard classical-album chart, is his first album of two-handed repertoire in 40 years.