Let g be a primitive root modulo a (n + 1)-bit prime p. In this paper we prove the uniformity of distribution of the Diffie-Hellman triples (gcursive Greek chi, gy, gcursive Greek chiy) as the exponents cursive Greek chi and y run through the set of n-bit integers with precisely k nonzero bits in their bit representation provided that k ≥ 0.35n. Such "sparse" exponents are of interest because for these the computation of gcursive Greek chi, gy, gcursive Greek chiy is faster than for arbitrary cursive Greek chi and y. In the latter case, that is, for arbitrary exponents, similar (albeit stronger) uniformity of distribution results have recently been obtained by R. Canetti, M. Larsen, D. Lieman, S. Konyagin [Israel J. Math, 120 (2000), pp. 23-46], and the authors.