We report on the generation and laser acceleration of bunches of energetic deuterons with a small energy spread at about 2 MeV. This quasimonoenergetic peak within the ion energy spectrum was observed when heavy-water microdroplets were irradiated with ultrashort laser pulses of about 40 fs duration and high (10-8) temporal contrast, at an intensity of 1019W/cm2. The results can be explained by a simple physical model related to spatial separation of two ion species within a finite-volume target. The production of quasimonoenergetic ions is a long-standing goal in laser-particle acceleration; it could have diverse applications such as in medicine or in the development of future compact ion accelerators.