We will first discuss joint work with Jörg Brüdern giving a sharp bound $p^{1/s+\varepsilon}$ for the smallest zero of a "random" homogeneous congruence in $s \ge 3$ variables modulo a prime $p$ (or, more generally, modulo a "rough" number). In the special case of small zeros of additive homogeneous congruences of degree $k$, for individual rather than random congruences I then want to show how to obtain a sharp bound $p^{1/k+\varepsilon}$ if $s$ is at least of order of magnitude $k \log k$.