We prove that the space of smooth rational curves of degree
e in a general complete intersection of multidegree (d1,...., dm) in Pn is
irreducible of the expected dimension if Σi=1m
di < 2n/3 and n is large
enough. This generalizes the results of Harris, Roth and Starr, and
is achieved by proving that the space of conics passing through any point
of a general complete intersection has constant dimension if Σi=1m
di is small compared to n
