Summary: Let $C\subset \Bbb {P}^n$ be a smooth curve defined over $\Bbb {F}_q$ with degree $d$ and genus $g$. Here we give conditions on $d,\, g,\, q$ which assure the existence of an isomorphic linear projection into $\Bbb {P}^3$ (case $n\ge 4)$ or a birational projection into $\Bbb {P}^2$ with only double points and defined over $\Bbb {F}_q$.