The role of HD cooling in the formation of primordial objects is examined by means of a great number of 1D models of the collapse of haloes, exploring a wide range of masses and virialization redshifts. We find that HD has very little effect upon the critical mass separating the objects which are likely to form stars from those which are not. We also find that, once the protostellar collapse has started, HD effects are quite negligible. Instead, HD effects can be important during the intermediate stage of gas fragmentation: objects below a certain mass scale (similar to 3 x 10(5) M-circle dot at z(vir). = 20 in our 'fiducial' case) can be cooled by HD down to T similar to 50-100 K, whereas H-2 cooling never takes the gas below T similar to 200 K. The lower temperature implies a reduction of a factor of similar to 10 in the Jeans mass of the fragmenting gas, and stars forming in such low-mass haloes are probably less massive than their Counterparts in larger haloes. We estimate the importance of this mode of star formation through a variation of the Press-Schechter formalism, and find that it never exceeds the contribution of haloes which are cooled by H2 only. Haloes where HD is important account at best for a fraction similar to 0.25 of the total primordial star formation. However, HD cooling might provide a channel through which long-lived low-mass stars could be formed in primordial conditions.