Fantasy No.1 for Cello and Piano is the first part of his Two Fantasies for Cello and Piano. This composition was commissioned in 1961 by the Canadian Broadcasting Corporation and premièred in 1963 by the Hungarian cellist, Laszlo Varga, with Pierre Souvairan at the piano. At that time the composer called it Sonata for cello and piano; it consisted of four movements. When he decided to rewrite this work, apart from the main theme of each movement, nothing was left of its original content. He also decided to join the first two movements together under the new title Fantasy No.1 and to join the last two movements under the title Fantasy No. 2.

Vladimir Orloff with his wife at the piano premièred the first Fantasy. The two Fantasies were played together the first time by the Japanese cellist, Tsuyoshi Tsutsumi at the Banff Music Festival in 1979.

The first part of the Fantasy No.1 is an Allegretto. The first theme is a dialogue between pizzicato chords in the cello and short melodic fragments in the piano. The comfortable mood of the opening later becomes more tense in rhythm and dynamics. After a short cadenza-like link in the cello, the quiet mood returns. The transition to the second part of the Fantasy is based on the opening pizzicato motif but this time the composer uses a very effective counterpoint in the cello of bowed melodies with simultaneous pizzicatos of the open strings. The second part of the Fantasy starts with a dotted two-bar motif which develops into a theme of an almost march-like character. Later themes of more melodic expression appear but the strong driving mood persists throughout until the almost percussive ending of the last five bars.