Let S-n,S-k denote the random geometric graph obtained by placing points inside a square of area n according to a Poisson point process of intensity 1 and joining each such point to the k = k (n) points of the process nearest to it. In this paper we show that if P (S-n,S-k connected) > n(-gamma 1) then the probability that S-n,S-k contains a pair of 'small' components 'close' to each other is o(n (c1)) (in a precise sense of 'small' and 'close'), for some absolute constants gamma(1) > 0 and c(1) > 0. This answers a question of Walters [13]. (A similar result was independently obtained by Balister.) As an application of our result, we show that the distribution of the connected components of S-n,S-k below the connectivity threshold is asymptotically Poisson.